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A bus completed first 50 miles of a 120-mile trip at an

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by BTGmoderatorLU » Sat Sep 07, 2019 12:43 am

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Source: e-GMAT

A bus completed first 50 miles of a 120-mile trip at an average speed of 20 mph. Then it took a halt of 30 minutes and completed the half of the remaining journey at an average speed of 35 mph. At what average speed it should complete the remaining journey so that the overall average speed of the whole journey becomes 20 mph?

A. 40 mph
B. 35 mph
C. 30 mph
D. 22.5 mph
E. 17.5 mph

The OA is E
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by GMATGuruNY » Sat Sep 07, 2019 6:02 am
BTGmoderatorLU wrote:Source: e-GMAT

A bus completed first 50 miles of a 120-mile trip at an average speed of 20 mph. Then it took a halt of 30 minutes and completed half of the remaining journey at an average speed of 35 mph. At what average speed it should complete the remaining journey so that the overall average speed of the whole journey becomes 20 mph?

A. 40 mph
B. 35 mph
C. 30 mph
D. 22.5 mph
E. 17.5 mph
At an average speed of 20 mph, the total time to travel the entire 120-mile trip = d/r = 120/20 = 6 hours.

At a speed of 20 mph. the time to travel the first 50 miles = d/r = 50/20 = 2.5 hours.
Time spent resting = 30 minutes = 0.5 hour.
Remaining distance = (total distance) - (distance already traveled) = 120-50 = 70 miles.
Time to travel half of the remaining 70 miles -- in other words, 35 miles -- at a speed of 35 mph = d/r = 35/35 = 1 hour.

Time to travel the last 35 miles = (total time) - (time spent thus far) = 6 - (2.5 + 0.5 + 1) = 2 hours.
Since the last 35 miles takes 2 hours, the speed for the last 35 miles = d/t = 35/2 = 17.5 mph.

The correct answer is E.
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by Scott@TargetTestPrep » Tue Sep 17, 2019 8:39 am
BTGmoderatorLU wrote:Source: e-GMAT

A bus completed first 50 miles of a 120-mile trip at an average speed of 20 mph. Then it took a halt of 30 minutes and completed the half of the remaining journey at an average speed of 35 mph. At what average speed it should complete the remaining journey so that the overall average speed of the whole journey becomes 20 mph?

A. 40 mph
B. 35 mph
C. 30 mph
D. 22.5 mph
E. 17.5 mph

The OA is E
We see that the bus has traveled 50 + 70/2 = 50 + 35 = 85 miles. Let x = the rate for the last 35 miles of the 120-mile trip. So the total time of the journey, including the 30-minute break, is 50/20 + 35/35 + 1/2 + 35/x = 4 + 35/x. We can create the equation:

120/(4 + 35/x) = 20

120/20 = 4 + 35/x

6 = 4 + 35/x

2 = 35/x

x = 35/2 = 17.5

Answer: E

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