Question

Noelle walks from point A to point B at an average speed of 5 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 6 kilometers per hour?

Answer 1

the speed at which Noelle walks from point B to A, v=7.5 kilometers per hour

Step-by-step explanation:

In this question we have given

average speed for the entire trip,S = 6 kilometers per hour

Speed of Noelle while walks from point A to B= 5 kilometers per hour

Therefore, time taken by Noelle to walks from point A to B,
`t_(1)=(d)/(5)`

Let us consider distance between A and B is d.

Therefore total distance covered in moving from point A to B and then moving back from point B to A, =
`d+d=2d`

Let v be the speed at which Noelle walks from point B to A

Therefore time taken by Noelle to walks from point B to A,
`t_(2)=(d)/(v)`

we know that average speed S is given as

`S=(x)/(t)`................(1)

here, x (=2d) is total distance

and t (=
`t_(1)+t_(2)` ) is total time

put values of S, x and t in equation 1

`6 =(2d)/((d)/(5)+(d)/(v)  )`

on solving we get,

v = 7.5 kilometers per hour

Therefore, the speed at which Noelle walks from point B to A, v=7.5 kilometers per hour