Problem Solving

Should I pick numbers for this question ? What is the best strategy ?

During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5 mile section of the expressway was 30 miles an hour , and his average speed for the remainder of the 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 ?

8.5%
50%
x/12 %
60/x %
500/x %

Ans E

Diatance = Time*Rate

For the 5 mile section Time=1/6 or 10 mins

For the remainder Distance= (x-5) Rate=60 So Time = (x-5)/60 or (x-5)mins

Total time = (x-5)mins + 10 mins

Option 2

Distance = x Rate=60 so Time = x/60 or x mins

This comes down to how much more is x+5 > x ?

I know I am missing something here. PLease help!! Exam is on Monday

Hi moneyman,

An easier way to look at this problem is to plug in numbers, so how about using 20 for X? With X = 20, Don took 10 minutes if he traveled 5 miles of the total distance at 30 miles/hour, plus 15 minutes for the rest of the trip at 60 miles/hour, for a total of 25 minutes.

However, if he traveled the entire distance at 60 miles/hour, it would only have taken him 20 minutes.

Thus, 25 minutes - 20 minutes = a difference of 5 minutes, and 5/20 = 25% (the difference between the two options). Now, find the answer that gives you this percentage, by plugging in the original number you chose for X (which is 20) and you'll see that the correct answer is choice E.

One last word of advice, no matter how good you are at algebra, you're better at arithmetic; so plug in whenever possible.

Good luck on your exam!

Thanks a lot Jim..I am very confortable with using numbers but I thought I could save some time by using this approach..but guess it dint work quite well..

Time taken with two seperate speeds:
5/30 +x-5/60 =x+5/60

Time if the speed 60miles/hr was constant:
x/60

Difference in two times : x+5/60 -x/60 =5/60

%age (5/60) / x/60 *100
=500/x

[E]

I'd just assume x = 5.

Then for 30 miles per hour on a 5 mile road, he averaged 30 miles per hour. The remaining road is 0 miles so the total average speed is 30 miles per hour.

If he traveled 60 miles per hour on that 5 mile road, then his average speed would be 60 miles per hour. This is double the 30 miles per hour rate.

So I plug in 5 in answer choices to see if I get 100% anywhere. Voila, E is answer.