How to Solve Quickly Speed Time And Distance Questions

Question 3 A motorboat covers a certain distance downstream in 30 minutes, while it comes back in 45 minutes. If the speed of the stream is 5 km/h what is the speed of the boat in still water?

Options:

A. 10 kmph

B. 5 kmph

C. 20 kmph

D. 25 kmph

Solution:   Let distance between two points = d kms
                   Let speed of boat in still water = s
                   Let speed of river = r

                  Now :

                  Downstream speed = s + r = s + 5

                  = \frac{d}{30} x 60 = 2d kmph

                  Upstream speed = s – r = s – 5

                  = d/45 x 60 = \frac{4d}{30} kmph

                  Solving s + 5 = 2d & s – 5 = 4d/3

                  2d – 5 = \frac{4d}{30} + 5

                  => 6d – 15 = 4d + 15

                  => d = 15 km

                  => s = 2d – 5 = 25 kmph

Correct Answer: D

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 A kid takes 6 hours for walking to a certain place and riding back. He would have taken 2 hours less by riding both ways. What will be the time required by him 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