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John is a trail runner who decides to take a day off work to run up

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John is a trail runner who decides to take a day off work to run up [#permalink]

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New post 20 Aug 2015, 03:33
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A
B
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E

Difficulty:

  15% (low)

Question Stats:

71% (01:08) correct 29% (00:45) wrong based on 123 sessions

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John is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 5 miles per hour and returns along the same route at an average speed of 7 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?

(A) 5.5

(B) 5.8

(C) 6.0

(D) 6.3

(E) 6.5

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Re: John is a trail runner who decides to take a day off work to run up [#permalink]

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New post 20 Aug 2015, 16:33
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Hi Gnpth,

These types of "weighted average" questions can be solved in a number of different ways. Here's how you can solve it by TESTing VALUES.

We're told that the distance UP the mountain and DOWN the mountain are the SAME, and that John's respective speeds are 5 miles/hour UP and 7 miles/hour DOWN. We're asked for the AVERAGE SPEED for the entire run. Since we're not given a distance, we can test ANY distance we like. By making the one-way distance 35 miles, we can make most of the 'math' easy to deal with.

UP:
Dist = (Rate)(Time)
35mi = (5mph)(T)
35/5 = T
7 hours = T

DOWN:
Dist = (Rate)(Time)
35mi = (7mph)(Time)
35/7 = T
5 hours = T

The formula for AVERAGE SPEED is...

Total Distance = (Average Speed)(Total Time)

The total distance is 35+35 = 70 miles and the average time is 7+5 = 12 hours...

70mi = (Av. Sp)(12 hours)
70/12 = Av. Sp.
35/6 =
5 5/6 miles/hour

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Re: John is a trail runner who decides to take a day off work to run up [#permalink]

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New post 20 Aug 2015, 22:07
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Gnpth wrote:
John is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 5 miles per hour and returns along the same route at an average speed of 7 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?

(A) 5.5

(B) 5.8

(C) 6.0

(D) 6.3

(E) 6.5


Since he runs the same distance, we can use the formula

Average Speed = 2ab/(a+b)

Average Speed = (2*5*7)/(5+7) = 5.8 mph

Answer (B)

Note that I am not a formula fan but some of these basic ones can come in handy. For more on this, check: http://www.veritasprep.com/blog/2015/02 ... -the-gmat/
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Re: John is a trail runner who decides to take a day off work to run up [#permalink]

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New post 16 May 2016, 14:44
to calculate average of 2 speeds a and b when distance is constant
Formula - 2ab/(a+b)
Here John's uphill speed = 5 mph
John's downhill speed = 7 mph
2*5*7/(5+7) = 70/12 = 5.833
Correct answer - B
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Re: John is a trail runner who decides to take a day off work to run up [#permalink]

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New post 04 Aug 2017, 20:19
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Re: John is a trail runner who decides to take a day off work to run up   [#permalink] 04 Aug 2017, 20:19
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