Noelle's walk

hansoo wrote: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?

a) 6.75
b) 7.00
c) 7.25
d) 7.50
e) 7.75

We can let the distance from point A to point B = d, so the entire trip is 2d.

Thus, the time to go from point A to point B is d/5. If we let r = Noelle’s walking rate from point B to point A, then her time is d/r. We can plug all of our values into the average rate formula:

average rate = (distance 1 + distance 2)/(time 1 + time 2)

6 = 2d/(d/5 + d/r)

6(d/5 + d/r) = 2d

6d/5 + 6d/r = 2d

6/5 + 6/r = 2

6/r = 4/5

30 = 4r

7.5 = r

Answer: D