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Difficulty:
25%
(medium)
Question Stats:
80% (02:20) correct
20%
(02:02)
wrong
based on 4972
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A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver did not make any stops during the 40-mile trip.)
(A) 65 mph
(B) 68 mph
(C) 70 mph
(D) 75 mph
(E) 80 mph
(A) 65 mph
(B) 68 mph
(C) 70 mph
(D) 75 mph
(E) 80 mph
09 Mar 2014, 15:05
Kudos
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SOLUTION
A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver did not make any stops during the 40-mile trip.)
(A) 65 mph
(B) 68 mph
(C) 70 mph
(D) 75 mph
(E) 80 mph
\(average \ speed=\frac{total \ distance}{total \ time}=\frac{40}{total \ time}=60\). This implies that for the average time to be 60 miles per hour, the total time must be 40/60 = 2/3 hours.
Now, the first 20 miles were covered in (time) = (distance)/(speed) = 20/50 = 2/5 hours.
Thus, the remaining 20 miles should be covered in 2/3 - 2/5 = 4/15 hours, which means that the remaining 20 miles should be covered at an average speed (distance)/(time) = 20/(4/15) = 75 miles per hour.
Answer: D.
A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver did not make any stops during the 40-mile trip.)
(A) 65 mph
(B) 68 mph
(C) 70 mph
(D) 75 mph
(E) 80 mph
\(average \ speed=\frac{total \ distance}{total \ time}=\frac{40}{total \ time}=60\). This implies that for the average time to be 60 miles per hour, the total time must be 40/60 = 2/3 hours.
Now, the first 20 miles were covered in (time) = (distance)/(speed) = 20/50 = 2/5 hours.
Thus, the remaining 20 miles should be covered in 2/3 - 2/5 = 4/15 hours, which means that the remaining 20 miles should be covered at an average speed (distance)/(time) = 20/(4/15) = 75 miles per hour.
Answer: D.
09 Mar 2014, 19:32
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Bookmarks
Answer = (D) 75 mph
Time = Distance / Speed
Setting up equation as shown in fig
Time = Distance / Speed
Setting up equation as shown in fig
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