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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Stacy and Katie plan to walk the 27-mile scenic route across
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BTGmoderatorDC
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A
B
C
D
E
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GMATGuruNY
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Since Stacy and Katie travel toward each other, they WORK TOGETHER to cover the 27 miles between them.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 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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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>
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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Jeff@TargetTestPrep
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We can create the equation: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
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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