Question

Ramesh could run a 100m race in 20 seconds. After training, he can finish the race in 15 seconds. By how much has he improved his speed?

Answer 1

Hint: We can find the speed of Ramesh before the training by dividing the distance with the time taken. After the training the speed can be obtained by dividing the distance with the new time. Then we can find how much he improved his speed by subtracting the initial speed from the speed after the training

Complete step-by-step answer:
It is given that the time taken by Ramesh to run a 100m race is 20 seconds.
Let the distance be \[d = 100m\] and the time taken before the training be ${t_1} = 20s$
We know that \[speed = \dfrac{{dis\tan ce}}{{time}}\]
So, the speed of Ramesh before the training is given by,
  ${v_1} = \dfrac{d}{{{t_1}}}$
On substituting the values, we get,
 $ \Rightarrow $ ${v_1} = \dfrac{{100}}{{20}}$
  $ \Rightarrow $ ${v_1}$ = 5m/s.
So, the speed before the training is 5m/s.
It is given that the time taken by Ramesh to complete the race after the training is 15 seconds.
So, the time taken after the training be ${t_2} = 15s$
So, the velocity of Ramesh after the training is given by,
 ${v_2} = \dfrac{d}{{{t_2}}}$
On substituting the values, we get,
 $ \Rightarrow {v_2} = \dfrac{{100}}{{15}}$
 $ \Rightarrow {v_2} = 6.667m/s$.
Now we can find how much he has improved his speed by finding the difference of the speed before and after the training.
 $ \Rightarrow {v_2} - {v_1} = 6.667 - 5$
 $ \Rightarrow {v_2} - {v_1} = 1.667m/s$
So, Ramesh’s speed has improved by 1.67 m/s.

Note: Speed is defined as the distance covered by a body in unit time. In this problem we can find the difference in speed by calculating the speed of both the cases and then subtracting it. We cannot find the difference in the time taken and divide the distance with the difference in the time taken. We must write the units and do the necessary unit conversions if needed.