Question

I walk each day to school. By what percentage would I need to increase my usual average speed in order for the journey to take 20% less time than usual? C:

Answer 1

25%

Explanation:

Let v, t be the current average speed and the time taken to reach the school respectively.

As distance = speed x time, so,

distance, d=vt...(i)

Let V be the new average speed in order to to take 20% less time than t.

So, time taken with speed V = t-20% of t = t- 0.2t= 0.8t

As distance is constant, so

d= V(0.8t)= 0.8Vt

hBy using equation (i), we have

0.8Vt = vt

0.8 V = v

V= v/0.8=1.25v

Therefore, the percentage increase in the average speed =
`(V-v)/(v)* 100`

`=(1.25v-v)/(v)* 100`

=25%

Hence, the percentage increase in the average speed is 25%.