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Ric begins walking up a mountain trail, ascending at a constant rate o [#permalink]

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08 May 2017, 11:45

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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?

Ric begins walking up a mountain trail, ascending at a constant rate o [#permalink]

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08 May 2017, 22:12

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In an hour, Ric would have walked 200 feet. When Josie begins walking down an hour later, the distance between Josie and Ric is 1500 feet. Since they walk in an opposite direction, the relative speed is the sum of their speeds Relative speed = Ric's Speed +Josie's Speed = 200+300 = 500ft/hour

To cover the distance between them, we need to use formula Time = Distance/Relative Speed

Time taken = 1500/500 = 3 hours.

Since we need to know the total distance walked by Ric, it would be 200(walked before Josie started) added to the three hours he walked when Rosie walked along(3*200 feet) Hence, Ric would walk 800 feet(Option C) _________________

Re: Ric begins walking up a mountain trail, ascending at a constant rate o [#permalink]

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08 May 2017, 23:25

Distance covered by Ric in 1 hour= 200*1= 200 Remaining distance between Ric and Josie= 1700-200=1500 ft Time taken by both of them to meet= \(\frac{Remaining Distance}{Relative Speed}\)= \(\frac{1500}{(200+300)}\)= \(\frac{1500}{500}\)= 3 hours

Total distance covered by Ric= 200+(3*200)= 200+600= 800

Answer: C.

Kudos please if you like my explanation!
_________________

Re: Ric begins walking up a mountain trail, ascending at a constant rate o [#permalink]

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09 May 2017, 05:18

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Distance covered by Ric in the first hour = 200 feet.

Distance between Ric and Josie after 1st hour = 1700 - 200 = 1500 feet.

When 2 object travel towards each other the rate of change (rate of object 1 + rate of object 2).

Hence, t = \(\frac{d}{(u+v)}\)

where, d = distance between 2 objects t = time taken by objects to cover the distance. u = rate or speed of object 1 v = rate or speed of object 2

based on above formula,

We get t = \(\frac{1500}{(200 + 300)}\)

t = \(\frac{1500}{500}\)

t = 3

Now, how much distance traveled by Ric in 3 hrs = 3 * 200 = 600 Total distance covered by Ric = 200 + 600 = 800 [where 200 is initial distance traveled by Ric in first hour]

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
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: Ric begins walking up a mountain trail, ascending at a constant rate o [#permalink]

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01 Nov 2017, 21:54

Hi all,

I have one question, is n't premise - "Sixty minutes later, Josie begins walking down the same trail, starting at a point 1,700 feet higher than Ric’s starting point" misleading? does n't the question tell the vertical height between ric's starting point and josie's starting point is 1700? in which case, the slope distance between them could be varying based on slope. I was scratching my head, how am i going to solve the problem without knowing the slope?