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Martha takes a road trip from point A to point B. She drives x percent
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15 Apr 2021, 00:58
15 Apr 2021, 00:58
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Martha takes a road trip from point A to point B. She drives x percent of the distance at 60 miles per hour and the remainder at 50 miles per hour. If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator?
(A) 110
(B) 300
(C) 1,100
(D) 3,000
(E) 30,000
(A) 110
(B) 300
(C) 1,100
(D) 3,000
(E) 30,000
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Martha takes a road trip from point A to point B. She drives x percent
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20 Apr 2021, 23:39
20 Apr 2021, 23:39
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GeminiHeat wrote:
Martha takes a road trip from point A to point B. She drives x percent of the distance at 60 miles per hour and the remainder at 50 miles per hour. If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator?
(A) 110
(B) 300
(C) 1,100
(D) 3,000
(E) 30,000
(A) 110
(B) 300
(C) 1,100
(D) 3,000
(E) 30,000
Let the total distance be \(d\)
For the first part;
Distance \(= \frac{xd}{100}\)
Speed = 60 m/h
Time \((t_1)= \frac{xd}{6000}\)
For the remaining part;
Distance \(= (1-\frac{x}{100})d\)
Speed = 50 m/h
Time \((t_2)= \frac{(100-x)}{5000}d\)
Average Speed \(= \frac{Total Distance}{Total Time} = \frac{d}{(t_1 + t_2)}\)
Solve further and you will have average speed as \(\frac{30000}{(600-x)}\)
Hence, option E
gmatclubot
Martha takes a road trip from point A to point B. She drives x percent [#permalink]
20 Apr 2021, 23:39
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