How to Solve Speed Distance and Time Questions Quickly

Question 3 : A freight train takes 5 hours to travel a certain distance. If it reduces its speed by 10 km/h, it would take 6 hours to cover the same distance. Find the original speed of the freight train and the distance it traveled.

                   Options

                   A. 60Km/h, 300 km

                    B. 23 Km/h, 1 km

                    C.45Km/h, 30 km

                    D.18km/h, 1 km

Solution: 

Let’s solve the problem step by step.

Let v be the original speed of the freight train in km/h and d be the distance traveled in km.

Given: The train takes 5 hours to travel distance d at speed v.

If the speed is reduced by 10 km/h, it takes 6 hours to travel the same distance d.

Step 1: Express the distance using the original speed and time.

d = v x 5

Step 2: Express the distance using the reduced speed and time.

d =(v − 10) x 6

Step 3: Set the two expressions for distance equal to each other.

v x 5 =(v − 10) x 6

Step 4: Solve for v.

5v = 6v −60
=> v = 60 km/h
v=60 km/h

Step 5: Find the distance d.

d = v x 5 = 60 x 5

= 300 km

Correct Answer – A

Question 4 Walking \frac{6}{7^{th}} \ of his usual speed, a man is 12 minutes late. What is the usual time taken by him to cover the distance?

Options:

A. 2 hrs

B. 1 hr 30 min

C. 1 hr 12 min

D. 39 min

Solution:    New speed of man = \frac{6}{7} \ of usual speed

As we know speed & time are inversely proportional

Hence, new time= \frac{7}{6} \ of usual time

Hence \frac{7}{6} \ of usual time- usual time= 12 minutes
⇒ \frac{1}{6} \ of usual time= 12 minutes

Therefore, usual time = 12×6 = 72 minutes

It means 1 hr 12 minutes

Correct Answer: C

Question 5:  Walking barefoot shanti takes 6 hours for walking to a certain place and coming back. She would have taken 2 hours less by riding both ways. What will be the time required by her  to walk both ways?

Options:

A. 6 hrs

B. 1 hr

C. 3 hrs

D. 8 hrs

Solution:    Time taken by the kid in walking to a certain place & riding back is 6 hrs

Time walk+ Time ride = 6

2 hrs of the time is reduced if he rides both the ways.

Time ride+ Time ride = 4

2× ride= 4

ride = \frac{4}{2} \

ride= 2

Now by putting the value of ride, we get

time walk + 2= 6

timewalk = 6-2 =4

Here we are finding the time taken by the kid if he walk both the ways

4+4=8

Therefore, he will take 8 hrs to walk both the ways.

Correct Answer: D