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
Stacy and Katie plan to walk the 27-mile scenic route across
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Since Stacy and Katie travel toward each other, they WORK TOGETHER to cover the 27 miles between them.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 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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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: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
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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