Problem Solving

During a trip on an expressway, Don traveled a total of x miles. His average speed at a certain 5-mile expressway was 30mph and his average speed for the rest of the trip was 60mph. His travel time was what percent greater than it would have been if he had traveled at 60 mph for the entire trip?

A.) 8.5%
B.) 50%
C.) x/12%
D.) 60/x%
E.) 500/x%



I got this question right by realizing that first of all, the answer must contain x, and second that it was probably larger than the smaller two. Furthermore, I realize that you could probably fill in a number for x, but was wonderful if there is a way to solve this using algebra.


By the way, OA is E.

Soln :

Total distance = x -- given
Travel time for 5 k.m run T1 = 5/30 = 1/6

Travel time for remaining trip T2 = (x-5)/60

Total Travel time is = T1 + T2 = (x+5)/60

Travel time for entire trip at 60 mph T = x/60
The final calculation

{[[(x+5)/60 - (x/60)]/(x/60)} *100 = 500/x %

Great Explanation Gaura! Thanks a lot.