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

BTGmoderatorDC wrote: ↑

Sun Apr 19, 2020 6:23 pm

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 cover the first 50 miles = 50/20 = 2.5 hours;

Time taken to cover the half of the remaining distance, i.e., (120 – 50)/2 (=35 miles) = 35/35 = 1 hour;

Say the remaining 35 miles is covered at s speed of x mph, thus, time take to cover 35 miles = 35/x hours

Total time spent = 120/20 = 6 hours

Again,

6 = 2.5 hours + 1/2 hour + 1 hour + 35/x

x = 17.5 mph

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorDC wrote: ↑

Sun Apr 19, 2020 6:23 pm

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 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

I had to take a halt to re-read the second sentence