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

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by BTGmoderatorDC » Mon Aug 13, 2018 9:25 pm
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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

OA C

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by GMATGuruNY » Tue Aug 14, 2018 1:47 am
BTGmoderatorDC wrote: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 swerve » Thu Aug 16, 2018 9:27 am
Please help me in understanding as to where I went wrong.

I tried as follows,

t = time taken
D = total distance
Ds = distance covered by Stacy in time "t"
Dk = distance covered by Katie in time "t"
Ss = Speed of Stacy.
Sk = Speed of Katie.

t = Ds/Ss = Dk/Sk
t = [D-Dk]/[(5/4)Sk = Dk/Sk
t = 4[27-Dk]/5Sk = Dk/Sk
108 = 5Dk

But, this is not the correct answer <i class="em em-confused"></i>
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by Jeff@TargetTestPrep » Mon Aug 20, 2018 10:52 am
BTGmoderatorDC wrote: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
We can create the equation:

1.25rt + rt = 27

2.25rt = 27

rt = 12

So Stacy will have walked 12 x 1.25 = 15 miles when they pass each other.

Answer: C

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