Problem Solving

During a trip on a expressway, Don drove a total of x miles. His average sppeed for a certain 5-mile section was 30miles per hour, and his average speed for the remainder of the trip was 60miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had travelled at a constant rate of 60 miles per hour for the entire trip?

8.5%

50%

(x/12)%

(60/x)%

(500/x)%


Answer is D
Please help, candies are awarded

gustavo.taucei wrote:During a trip on a expressway, Don drove a total of x miles. His average sppeed for a certain 5-mile section was 30miles per hour, and his average speed for the remainder of the trip was 60miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had travelled at a constant rate of 60 miles per hour for the entire trip?

8.5%

50%

(x/12)%

(60/x)%

(500/x)%


Answer is D
Please help, candies are awarded

Plug in x = 60.
Time for 5-mile distance = d/r = 5/30 = 1/6 hour.
Time for remaining 55 miles at 60mph= d/r = 55/60 = 11/12 hour.
Total time = 1/6 + 11/12 = 13/12 hour.
Total time for 60 miles at 60mph = 60/60 = 1 hour.
% time increase = (Difference between longer and shorter times)/(Shorter time) * 100 = (13/12 - 1)/1 * 100 = 100/12 = 50/6. This is our target answer.

Now we plug x=60 into all the answer choices to see which yields our target of 50/6.

Only answer choice E works:
500/x = 500/60 = 50/6.

Please check the OA. Answer choice D is not correct.

youre absolutely right

question E is the correct one

i appreciate your help!