Speed,Time and Distance Quiz-4

Using the above standard formula -

X = 324 hours

Y = 225 hours

Speed of A : Speed of B = \sqrt{Y} : \sqrt{X} = \sqrt{225}:\sqrt{324} = 15/18

Total distance travelled by ferrari in 12 hours  = (35+37+39+.....upto 12 terms)

This is an A.P,

a=35, number of terms,

n= 12, d=2.

Required distance    = 12/2[2 x 35+{12-1) x 2]

=6(70+23)

= 552 kms.

Number of gaps between 41 poles = 40

So total distance between 41 poles = 40*50

=>   2000 m =  2 km

In 1 minute the train is moving = 2 km/minute.

Speed in hour = 2*60 = 120 km/hour

Let the length of the train be x metres.

Then, the train covers x metres in 8 seconds and (x + 180) metres in 20 seconds.

x/8  = \frac{x+180}{20}

<->   20x = 8(x + 180)

<->   x = 120.

----->  Length of the train = 120 m.

Speed of the train  ( \frac{120}{8}) = m/sec = 15 * 18/5 m/sec = kmph = 54 kmph.

Relative speed of the trains

= (82 - 64) km/hr = 18 km/hr

= ( 18 * 5/18 ) m/s = 5 m/sec

Time taken by the trains to cross each other

= Time taken to cover (200+120) m at 5 m/sec = ( 320/5) sec = 64 sec

Relative Speed = ( 280/9 ) m/sec  = (280/9 * 18/5 ) kmph = 112 kmph

Speed of Vande Bharat Express = ( 112- 50 ) kmph = 62 kmph

Speed of the Mike Hailwood = 60km/hr.

Distance covered in 1st 2 hours = 60 km.

He increased his speed in every 2 hours by 3 km/hr.

Distance covered in every 2 hours will be, 60, 63, 66,... upto 12 terms.(for 24 hours).

The above series is an A.P series;

Sum of first n terms = (n/2)(2a+(n-1)d)

Here, a = 60, d = 3 and n = 12.

Sum of first 12 terms = (12/2)(2(60)+(11)3) = 6(120 + 33) = 6(153) = 918.

Hence, Mike Hailwood covers 918 km in 24 hours.

Time taken to go from home to hostel = d/60

Time taken to drive at 25 miles from hostel to home = d/25

Time to drive through bypass = (d/2 + 5)/50

Total time taken from hostel to home = d/25 + (d/2 + 5)/50

According to the question,

d/25 + (d/2 + 5)/50 = d/60 + 30/60 (Convert time from minutes to hours)

On solving, we get d = 30

Total distance travelled = 2d + 5 = 65miles

Meeting at a starting point means it doesn't matter if they start in the same direction or OPPOSITE.

Speed of Alia Bhatt= 14 rph

Speed of katrina Kaif = 18 rph

The ratio of Speeds = 7 : 9

So ratio of Distances also = 7 : 9

They meet when Alia Bhatt travels 7 rounds and Katrina Kaif travels 9 rounds.

for 14 rounds →  Seeta takes 60 minutes

for 7 rounds → 60/2 = 30 minutes

They meet after 30 minutes at starting point ‘t’.

 

Distance travelled by the Porsche in 14 min 30 sec could be travelled by sound created by guns in (15 min – 14 min 30 sec) = 30 sec.

Porsche travels = 330 × 30 in 141/2 min.

Speed of the Porsche per hour = (330×30×2×60)/(29×1000)

= (99×12)/29

= 1188/29

= 4028/29km/hr