Yellow22 wrote:
During a trip on an expressway, Don drove x miles.His average speed on a certain 5 mile seciton was 30 miles per hour and his average speed of the remainder ofthe trip was 60 miles 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
A) 8.5 %
B) 50%
C) x/12%
D) 60/x%
E) 500/x%
Long word problem with a variable in the choices - perfect situation for picking numbers.
Let's let x=15 to keep things simple.
So, he drove 5 miles at 30mph and 10 miles at 60mph.
time = dist/rate, so he spent 5/30 + 10/60 = 1/6 + 1/6 = 1/3 of an hour = 20 minutes total.
If he had travelled at 60mph for the entire 15 miles, his time would have been 15/60 = 1/4 hour = 15 minutes.
The question is "His travel time for the x mile trip was what percent greater", so we use the percent change formula:
% change = (amount of change / original amount) * 100%
= (20-15)/15 * 100% = 5/15 * 100% = 1/3 * 100% = 33 1/3 %
Plugging x=15 into the choices:
A) 8.5 %... nope
B) 50%... nope
C) x/12%.... 5/4 of 1%... nope
D) 60/x%... 4%... nope.
E) 500/x%... 500/15 = 100/3 = 33 1/3.. yay! Choose (E).