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Stacy and Katie plan to walk the 27-mile scenic route across

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by BTGmoderatorLU » Thu Jan 24, 2019 2:56 pm

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Source: Veritas Prep

Stacy and Katie plan to walk the 27-mile scenic route across Malibu, starting at opposite ends of the route at the same time. If Stacy's rate is 25% faster than Katie's, how far will Stacy have walked when they pass each other?

A. 12
B. 13.5
C. 15
D. 16.25
E. 17.33

The OA is C
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by GMATGuruNY » Thu Jan 24, 2019 2:59 pm
BTGmoderatorLU wrote:Source: Veritas Prep

Stacy and Katie plan to walk the 27-mile scenic route across Malibu, starting at opposite ends of the route at the same time. If Stacy's rate is 25% faster than Katie's, how far will Stacy have walked when they pass each other?

A. 12
B. 13.5
C. 15
D. 16.25
E. 17.33
Since Stacy and Katie travel toward each other, they WORK TOGETHER to cover the 27 miles between them.
Since Stacy is 1/4 faster than Katie, for every 4 miles that Katie travels, the distance traveled by Stacy = 4 + (1/4)(4) = 5 miles.
Thus, of every 9 miles traveled when Stacy and Katie work together, Stacy travels 5 miles.
Implication:
Stacy will travel 5/9 of the 27-mile distance:
(5/9)(27) = 15 miles.

The correct answer is C.
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by Scott@TargetTestPrep » Thu Jan 31, 2019 5:39 pm
BTGmoderatorLU wrote:Source: Veritas Prep

Stacy and Katie plan to walk the 27-mile scenic route across Malibu, starting at opposite ends of the route at the same time. If Stacy's rate is 25% faster than Katie's, how far will Stacy have walked when they pass each other?

A. 12
B. 13.5
C. 15
D. 16.25
E. 17.33

The OA is C
If we let r = Katie's rate, then Stacy's rate is 1.25r. Both women start at the same time, so the time t is the same for each woman. .We can create the equation:

1.25rt + rt = 27

2.25rt = 27

rt = 12

Thus, Katie will have walked 12 miles when they pass each other, so Stacy will have walked 12 x 1.25 = 15 miles.

Answer: C

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