SajjadAhmad wrote:

Ric begins walking up a mountain trail, ascending at a constant rate of 200 feet per hour. Sixty minutes later, Josie begins walking down the same trail, starting at a point 1,700 feet higher than Ric’s starting point. If Josie descends at a constant rate of 300 feet per hour, how many feet will Ric have ascended when the two meet?

A. 600

B. 680

C. 800

D. 850

E. 900

We have a converging rate problem in which we can use the following formula:

distance of Ric + distance of Josie = 1700

We are given that Ric’s rate is 200 ft/hr and that Josie’s rate is 300 ft/hr. Since Josie began 60 minutes, or 1 hour, after Ric, we can let Josie’s time be t hours and Ric’s time be (t + 1) hours. Thus, Ric’s distance is 200(t + 1) = 200t + 200 and Josie’s distance is 300t. Let’s now determine t:

Ric’s distance + Josie’s distance = 1700

200t + 200 + 300t = 1700

500t = 1500

t = 3

Thus, when the two meet, Rick will have ascended 200(3 + 1) = 800 feet.

Answer: C

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