# Speed Time and Distance Questions and Answers

## Speed, Time and Distance Questions and Answers

On this  page we are going to discuss Speed,  Distance and Time Questions and Answers along with basic definition to help students understand the topic and prepare well.

## Relationship Between Speed Time & Distance

1. Speed = Distance/Time – This means Speed is equal to Distance covered by time taken. It shows us how fast or slow an object moves
2. Speed is Inversely proportional to Time and directly proportional to Distance, Time being constant in this case.
3. Distance = Speed X Time, and
4. Time = Distance / Speed, as speed increases distance is covered faster and hence time decreases, and vice versa. Using the above formulas  any basic problems can be solved, and unit conversion must be kept in mind.

Speed, Distance and Time can be expressed in different units:

##### Units of Speed ,Time and Distance

Time: seconds(s), minutes (min), hours (hr)

Distance: (meters (m), kilometers (km), miles, feet

Speed: m/s, km/hr

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1. A Van of robbers is noticed by a Cop from a distance of 200 m. The robbers leave the van and start running and the cop chases them. The robbers and the cop run at the rate of 10 km and 11 km per hour respectively. After 6 minutes what will be the distance between them?

50 meter

50 meter

13.38%

100 meter

100 meter

57.3%

110 meter

110 meter

16.76%

None of the above

None of the above

12.56%

Relative speed of cop with respect to robbers = (11 - 10) = 1 Km/hr.

Now the relative distance covered by cop in 6 min

= Speed x Time = 1 x 6/60

=1/10km = 100m

The distance between the Cop and Robbers after 6 min = 200 - 100 = 100 m.

2. Aakash is quite a sportsperson so he like to travel some part of his journey on foot at 4 km/hr and some part on cycle at 9 km/hr to his office covering a total distance of 66 km in 9 hours. What is the distance travelled on foot?

16.25 km

16.25 km

16.12%

25 km

25 km

14.93%

12 km

12 km

63.28%

57 km

57 km

5.67%

Assume the time in which he travelled on foot = x hour
Time required to travel on cycle = (9 - x) hr

the total distance = 66 km
Hence,
4x + 9(9-x) = 66
=> 5x = 15
=> x = 3

so distance travelled on foot = 4(3) = 12 km. Option 3 is the correct answer.

3. An Airbus A350 is flying north at 500 kmph passes over a city at 12 noon. A Spice jet Airbus is flying east at the same attitude passes over the same city at 12.30 pm. The speed of Spice jet is at 400 kmph flying east. How far apart are the two planes at 2 pm to the nearest 100 km?

600 km

600 km

17.68%

1000 km

1000 km

13.05%

1100 km

1100 km

34.12%

1200 km

1200 km

29.09%

1300 km

1300 km

6.06%

The Airbus A350 flying north would have travelled for 2 hours at 2 PM.

It travels at 500 kmph.

Hence, the Airbus flying north would have covered 1000 kms from the city at 2 PM.

The Spice jet flying east would have travelled for 1.5 hours at 2 PM.

It travels at 400 kmph.

Hence, the Spice jet flying east would have covered 1.5*400 = 600 kms from the city at 2 PM.

Both the Airbus and Spice jet are flying at right angles to each other.

The shortest distance between the two planes is the length of the hypotenuse of the right triangle whose legs are the distances covered by both of them.

Hence, distance =   = 1166 km

4. Two cyclists start together to travel to a certain destination, one at the rate of 4 kmph and the other at the rate of 5 kmph. Find the distance if the first cyclist arrives half an hour after the second cyclist

2 km

2 km

26.65%

10 m

10 m

29.17%

10000 m

10000 m

25.78%

1000 m

1000 m

18.4%

Assume the distance to be X km.
=>Time for the first rider = X/4.
Similarly, time for the second cyclist = X/5.
Given that: X/4 – X/5 =X/20
=> X/20= 1/2 => X=10 km = 10000 m. So Option 3 is the correct answer.

5. In still water of river a captain is sailing a ship at the speed of 20 mph. Once water starts moving, ship takes 5 hr 30 mins to cover a distance of 50 miles and come back. Find the speed of the water.

6 mph

6 mph

28.1%

8 mph

8 mph

35.32%

5 mph

5 mph

18.86%

2 mph

2 mph

17.72%

Let us assume,
Speed of water be x.
Now,
Distance =50 miles, Speed=20 mph (in still water)
Speed of the ship along with speed of water=10+x
Speed of the ship against the speed of water=10-x
Time=5 hr 30 minutes.
T=D/S
5.5= $\frac{50}{20+x} + \frac{50}{20-x}$
5.5=$\frac {50(20-x)+50(20+x)}{(20+x)(20-x) }$
5.5 = $\frac {2000}{400- x^{2}}$
$2200-5.5x ^{2}=2000$
$5.5x ^{2}=200$
$X^{2}=36.36$
X=6.06 rounding off to 6

6. Simran like to walk to a town at 3 and half kmph, rest there for 45 minutes and ride back at 7 and half kmph. If the total time spent by simran is 6 hrs 37 min find the distance to the town.

14 km

14 km

62.18%

7 km

7 km

15.13%

17 km

17 km

15.29%

4 km

4 km

7.39%

Since the distance covered is same,
Average speed = 2*a*b/ (a+b), where a & b are respective speeds of to and fro journey.
Avg speed = 2*3.5*7.5/ (3.5+7.5) = 4.77 km/hr (approx.)
The total time = 6 hrs 37 minutes.
Rest = 45 minutes
Hence, travel time = 6 hrs 37 minutes - 45 minutes = 5 hrs 52 minutes $=5\frac{52}{60} = 5\frac{13}{15}$
D = S * T = 4.77 *$5\frac{13}{15}$
= 4.77 *$\frac{88}{15}$  = 28 Km
This is the total distance, that is, to and fro.
Hence distance to town = 28/2 = 14 Km.
Option 1 is the correct answer.

7. A bus travels at 54km/h while moving but after accounting for stopping time, to let passengers on and off the coach, it averages a speed of 45km/h. How many minutes does the bus stop for each hour?

1 min

1 min

9.03%

10 min

10 min

45.48%

3 min

3 min

21.57%

9 min

9 min

23.91%

In one hour without stopping, the bus would have travelled 54km. Once stopping is factored in, the bus actually travels 45km. So it travels 9km less far as a consequence.
Distance/Speed = Time
9km/54kmph = 0.16 hours
0.16 * 60 = 10 minutes
So the bus stops for ten minutes in every hour on average.
Option 3 is the correct answer.

8. Jack is a businessman who owns an expensive yacht which can cover distance in 1 hour, while it returns in 2 hours. If the speed of the stream is 4 km/h, what will be yacht’s speed in still water?

30 km/hr

30 km/hr

9.65%

12 km/hr

12 km/hr

74.9%

16 km/hr

16 km/hr

10.04%

40 km/hr

40 km/hr

5.41%

Let ‘s’ km/h be the speed of Jack’s yacht.
Then, 1(s+4) = 2(s-4) → s=12 km/h
So option 2 is the correct answer.

9. To get to a business meeting, John drove m miles in h hours, and arrived 1/2 hour early. At what speed should he have driven to arrive on exact time?

m/2h

m/2h

15.81%

2m/(2h+1)

2m/(2h+1)

30.04%

2m/(2h-1)

2m/(2h-1)

47.04%

2m-h/2h

2m-h/2h

7.11%

To arrive at the business meeting exactly on time, John should have driven at a speed of 2m / (2h - 1) miles per hour. This formula takes into account the distance he needs to cover (m miles) and the adjusted time he should have taken to arrive on time (2h - 1 hours).
So option 3 is the correct answer.

10. Romita and supriya start at the same time to ride from mewar to chittorgarh, 80 km away. Romita travels 6kmph slower than supriya. Supriya reaches mewar and at turns back meeting Romita 20km from chittorgarh. Find Romita’s speed?

2.1Km/h

2.1Km/h

8.99%

24 Km/h

24 Km/h

55.76%

6 Km/h

6 Km/h

15.44%

15 Km/h

15 Km/h

19.82%

Distance between Mewar to chittorgarh = 80 km

Speed of Romita = Speed of supriya - 6

Ratio of distance = 80 : 80+20

= 80 : 100 = 4 : 5

Difference  = 1

So, 1 unit = 6

Value of 4 unit(distance covered by Romita) = 24 km/hr

Speed of Romita = 24 km/hr

11. Japan’s minister had recently launched an express train which on Monday was travelling at 72km per hour crosses a newly built platform in 30 seconds. Determine the length of the platform in m?

600 m

600 m

58.29%

360 m

360 m

14.09%

420 m

420 m

7.18%

600 m

600 m

20.44%

Length of the platform = speed of train * extra time taken to cross the platform.
So length of platform = 72 kmph * 30 seconds
Convert 72 kmph into m/sec
1 kmph = 5/18 m/s
Therefore 72 kmph = 5/18∗72 = 20 m/sec
Hence the length of the platform = 20 m/s * 30 sec = 600 meters.

Option 1 is the correct answer.

12. Aria is the lead runner of the famous school in her city. Briana is allowed a lead of 7 meters to finish the race by Aria who runs 25 percent faster than Briana. How long is the race (in meters)?

10

10

13.73%

20

20

13.38%

35

35

68.31%

45

45

4.58%

Aria runs 25 percent faster than Briana.
If Briana runs 100 m in a time interval given, Aria will run 125 m in the same time.

Assuming.

If Aria runs 5 m in a given time, then Briana will run 4 m in the same time.

If the length of a race is 5 m, then Aria can give Briana a start of 1 m (Aria can allow Briana to start 1 ahead of the start point) so they end the race.
The ratio of length of start given: length of race: 1: 5

As given in the question,
The start given in the question is 7 m.
Finally, length of the race will be 7 * 5 = 35 m.

13. Kane while going to his supermarket covered a distance of 340 km between city Arizona and city Baker’s way taking a total of 5 hours. If part of the distance was covered at 60 km per hour speed and the remaining distance at 80 km per hour, how many hours did he travel at 60 km per hour?

2 hours 30 minutes

2 hours 30 minutes

16.26%

3 hours

3 hours

67.82%

2 hours

2 hours

11.07%

45 minutes

45 minutes

4.84%

Assume that Kane travel in x hours at 60 km per hour.
As the total time taken to cover 340 miles is 5 hours, Kane would have travelled (5 - x) hours at 80 km per hour.
Distance covered at 60 km per hour = Speed * time = 60 * x = 60x km.
Distance covered at 80 km per hour = Speed * time = 80 (5 - x) = 400 - 80x km.
Total distance covered = Distance covered at 60 km per hour + Distance covered at 80 km per hour.
So, the total distance = 60x + 400 - 80x.
Total distance travelled = 340 km
340 = 60x + 400 - 80x
20x = 60 or x = 3 hours.
Option 2 is the correct answer.

14. Ram and Raghu have joined shooting classes recently where Raghu practices and hold the gun which is fired at a distance of 6.64 km away from Ram. He hears the sound 20 seconds late. Then the speed of the sound is?

664 m/s

664 m/s

9.7%

634 m/s

634 m/s

10.07%

332 m/s

332 m/s

76.12%

432 m/s

432 m/s

4.1%

6.64 km = 6640 m
He hears the sound 20 seconds late.
We know, Speed = Distance/Time
Therefore the speed of the sound = 6640/20 = 332 m/s.

Option 3 is the correct answer.

15. Hari asked his mathematics teacher an interesting question that the ratio between the speeds of two roadways buses is 11: 9. If the second bus runs 270 km in 15 hours, then the speed of the first bus is?

23 km/h

23 km/h

9.06%

11 km/h

11 km/h

10.45%

2 km/h

2 km/h

5.23%

22 km/h

22 km/h

75.26%

Let the speeds of the two buses be 11x and 9x respectively.
Speed of the second bus = 270/15 = 18 km/hr (∵ Speed = Distance/Time)
⇒ 9x = 18
⇒ x = 18/9 = 2
Speed of the first bus = 11x = 11 × 2 = 22 km/hr
Therefore the speed of the first bus = 22 km/hr
Option 4 is the correct answer.

16. Rajan goes to his office by metro. One day while travelling in metro he notices that he can count 24 lamp posts in one minute. At what speed is the metro travelling if they both are 50 meters apart from each other?

75 km/h

75 km/h

11.29%

77 km/h

77 km/h

12.1%

69 km/h

69 km/h

66.94%

70 km/h

70 km/h

9.68%

There are 24 lamp posts and the gap between two is 50 meters
Total distance = 23 × 50 = 1150 m
Time = 1 min= 60 sec
Now, speed = Distance/Time
⇒ Speed = 1150/60 = 19.16 m/s
⇒ Speed = (19.16 × 3600)/1000 = 69 km/hr
Option 3 is the correct answer

17. Mandeep’s newly owned Ashok Leyland bus covers a distance of 660 metres in 1 minute where as his dad’s car covers a distance of 44 kms in 50 minutes. The ratio of their speeds is:

3 : 4

3 : 4

74.41%

4 : 3

4 : 3

12.99%

5 : 4

5 : 4

5.91%

3 : 5

3 : 5

6.69%

We know that speed is defined as:
Speed=distance travelled/time required to travel the distance
For the bus, it covers a distance of 660 meters in 1 minute (or 60 seconds).
From the above formula,
Speed of bus (SB) =660 meters /second
Or, speed of bus SB = 11 meters/second
Similarly, for the car, it covers a distance of 44 km (or 44 × 1000 meter) in 50 minutes (or 50 × 60 seconds).
From the above formula,
car speed (CS) =44000 meters / (50×60) second
Or, speed of car SC = 44/3 meters/second
Bus speed (BS)/ car speed (CS) =11/44/3=3/4
Or, Speed of bus: speed of car = 3: 4

Option 1 is the correct answer.

18. In the beautiful city of Kerala a science student finds out that a city rickshaw can travel a distance of 715 km at a steady speed. If the speed of the rickshaw had been 10km/hr, then it would have taken 2 hours less to cover the same distance. What is the initial speed of the auto?

45 km/h

45 km/h

12.32%

50 km/h

50 km/h

18.48%

65 km /h

65 km /h

12.8%

55 km/h

55 km/h

56.4%

Assuming that the constant speed be x km/hr.
715/x-715/(x+10) =2⇒1/x-1/(x+10) =2/715
⇒(x+10)-x/x(x+10) =2/715⇒x(x+10) =3575
$x^{2}+10x-3575=0$$x^{2}+65x-55x-3575=0$
⇒x(x+65)-55(x+65) =0
⇒(x+65) (x-55) =0
⇒x=55.
∴Original speed of the car is 55km/hr.

Option 4 is the correct answer.

19. A and B begin all the while from a sure point in North and South bearings on engine cycles. The velocity of A is 80 km/hr and that Of B is 65 km/hr. What is the separation in the middle of A and B following 12 minutes?

14.5km

14.5km

15.98%

29 km

29 km

70.78%

36.2 km

36.2 km

9.13%

39 km

39 km

4.11%

required distance = sum of distance covered by A and B
= {(80*12/60) + (65*12/60)} = (16+13) = 29 km

Option 2 is the correct answer.

20. The proportion between the rates of going of Arash and Bunty is 2:3 and in this manner Arash takes 10 minute more than the time taken by Bunty to reach a destination. In the event that Arash had strolled at two fold speed, he would have secured the separation in

30 min

30 min

9.23%

20 min

20 min

23.59%

15 min

15 min

62.05%

40 min

40 min

5.13%

Ratio of time taken by Arash and Bunty = 1/2: 1/3
Suppose Bunty takes x min. Then, Arash takes (x+10) min.
∴(x+10): x= 1/2: 1/3 = 3:2 ⇒ x+10/x = 3/2 ⇒ 2x+20 = 3x ⇒x = 20
Thus Bunty takes 20 min. and Arash takes 30 min.
AT double speed A would covers it in 15 min.

Option 3 is the correct answer.

21. Raghuveer is pacing at a speed of 6 km/hr crosses a bridge in 18 min. What is the length of the bridge(in meters)?

1800 m

1800 m

81.67%

1500 m

1500 m

10%

1200 m

1200 m

5.83%

1900 m

1900 m

2.5%

Raghuveer’s speed = 6 km/hr = 6x 5/18 m/sec = 5/3 m/sec

Length of the bridge = (5/3) x18x60 = 1800 m

Option 1 is the correct answer.

22. Sarita is web developer and she travels a lot, recently she had left for Jamnagar from Raipur at 6 AM. For 2 hours, she travelled at the rate of 100 km/hr. After that, she declined her speed to 60 km/hr. Determine time when Sarita is going to reach Jamnagar. If the distance between two cities is 680 km?

11:30 am

11:30 am

8.44%

11:55pm

11:55pm

5.78%

4:00pm

4:00pm

80%

12:30am

12:30am

5.78%

Distance covered in 2 hours = 100 x 2 = 200 km

To cover the remaining distance the time will be taken = (680 - 200)/60 = 480/60 hrs = 8 hrs

The Total time = 2 + 8 = 10 hrs

Sarita will reach Jamnagar at 4:00 P.M.

23. Saroj runs around a circular field at a rate of 6 rounds/hour whereas Arita walks around the same field at the rate of 1 round/hour. If they both start in the same direction from the same point at 7:30 AM at what time will they first cross each other?

8:15 am

8:15 am

9.52%

7:50 am

7:50 am

10.48%

8:00 am

8:00 am

10%

7:42 am

7:42 am

70%

Speed of Saroj w.r.t Arita = 6 - 1 = 5 rounds per hour
At this speed the time taken to complete 1 round = 1/5 = 12 min i.e. 7:30am plus 12 minutes is equal to 7:42am.

Option 4 is the correct answer.

24. Ramu is a loyal worker in a cement company where he daily travels and covers distance of 80km in 12 hours. He decided to travel some part of his journey on roadways bus at 6 km/hr and some part by cng rickshaw at 12 km/hr. What is the distance travelled on roadways bus?

22 km

22 km

9.52%

85 km

85 km

10.95%

64 km

64 km

73.81%

96 km

96 km

5.71%

Let x km be the distance travelled on roadways bus
The total distance covered by cng rickshaw = (80 - x) km
So, x/6 + (80 - x)/12 = 12
12x + 6(80 - x) = 12
x = 64 km

Option 3 is the correct answer

25. Sohan loves travelling and he has bought a new electric car for which he had dreamed about that can travel at the speed of 40 km per hour. How long will it take to cover 330 kilometres if the speed is 50% increased?

5 hours 30 min

5 hours 30 min

79.28%

6 hours 20 min

6 hours 20 min

11.26%

5 hours 29 min

5 hours 29 min

6.31%

4 hours 12 min

4 hours 12 min

3.15%

Original speed is 40km per hour
If the speed is increased by 50%, then the new speed is = 150 % of 40= 60km per hour
It is given that the distance to be covered is 330 kms.
The total time taken to cover 330 kilometres distance at 60 km per hour is
330 / 60 = 5.5 hours = 5 hrs 30 minutes
Hence, if the person is increased by 50%, it will take 5 hrs 30 minutes to cover 330 km distance.

Option 1 is the correct answer.

26. Seema lives in Delhi and she is a travel blogger and a passionate traveller who travels 100 kilometres at a speed of 50 km per hr by her car, the she covers 800 km by ship at a speed of 40 km per hr, and then she travels 600 km by train at a speed of 80 km/hr and 500 km by helicopter at 400 km per hr. find the average speed for the entire journey?

65.04 km per hr

65.04 km per hr

76.32%

60 km per hr

60 km per hr

11.58%

62.60 km per hr

62.60 km per hr

7.89%

61.20 km per hr

61.20 km per hr

4.21%

The total distance covered= (600 + 800 + 500 + 100) km = 2000 km
the total time =

$\frac{600}{80} +\frac{800}{40} + \frac{500}{400} + \frac{100}{50} = \frac{123}{4}$

So, the average speed = $\frac{2000*4}{123}$

Option 1 is the correct answer.

27. An electric bike goes at the speed of 50 km/h when it is not modified and runs at 60 km/h when modified. After modifying the electric bike it covers a distance in 6 h. How much time will the new electric SUV will take to cover the same distance when not modified?

8.2h

8.2h

8.41%

6.5h

6.5h

9.73%

7.2h

7.2h

76.11%

2.5h

2.5h

5.75%

modifying speed of the electric bike = 60 km/h

Distance it covers in 6h. = (60 * 6) km = 360km

The time taken to cover 360 km when it is not modified = (360 / 50) = 7.2h

Option 3 is the correct answer.

28. After every 1 hour a sports bike increases its speed by 2km. If the distance travel in the first hour was 45 km, find the total distance travelled in 12 hours?

600km

600km

12.21%

643km

643km

9.39%

633km

633km

6.1%

672km

672km

72.3%

In 12 hours the distance travelled = (45 + 47 + 49 + ..... up to 12 terms.)
It is an AP which has its first term as a = 45, number of terms, n = 12, common difference, d = 2.
Distance that is required =

12/2 [2*45 + (12-1)*2] = 6 (90 + 22) = 672 km.

Option 4 is the correct answer.

29. A brand new motor boat has a speed of 65 km/h and river is flowing at a rate of 5 km/h.The boat covered 140km while moving with the stream. How much distance will the boat cover when is goes against the stream at the same time?

120

120

42.01%

180

180

11.42%

60

60

42.47%

100

100

4.11%

Let x be the distance to be covered by the boat when it goes against the stream.

Motor boat goes down the river at a speed of 65 + 5 = 70 km/h and up the river at a speed of 65 - 5 = 60km/h.

30. Hirendra and his wife reside in the outskirts of Mumbai. Hirendra and his wife were playing a game where they are separated by a distance of 81 km away and begin to move towards each other at the same time. If Hirendra covers 6 km per hour to his wife at 3 km per hour, how far will his wife have to commute when they meet?

27 km

27 km

82.97%

36 km

36 km

7.86%

45 km

45 km

4.8%

55 km

55 km

4.37%

Time taken to meet = (Distance) / (speed) = 81/ (3 + 6) = 9 hours

So, Hirendra’s wife has travelled = 9 x 3 = 27km.

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