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

BTGmoderatorDC wrote: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

OA E

Source: e-GMAT

Time taken to complete first 50 miles of a 120-mile trip at an average speed of 20 mph = 50/20 = 2.5 hours;
Time taken for halt = 30 minutes = 0.5 hours;
Time taken to complete the half of the remaining journey [1/2 of (120 – 50) = 1/2 of 70 = 35 miles] at an average speed of 35 mph = 35/35 = 1 hour;

Total time taken so far = 2.5 + 0.5 + 1 = 4 hours

Distance remaining = 120 – 50 – 35 = 35 miles

To attain an average speed of 20 mph, the bus must complete 120 miles in 120/20 = 6 hours

Thus, the bus must complete the remaining distance (35 miles) in 6 – 4 = 2 hours

Thus, the average speed at which the bust must run for the remaining distance (35 miles) = 35/2 = 17.5 mph

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorDC wrote: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

OA E

Source: e-GMAT

We see that the bus has traveled 50 + 70/2 = 50 + 35 = 85 miles. Let x = the time 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