SOLUTION: Hi, this is a question from the Math Review for the GRE General Test. Two cars started from the same point and traveled on a straight course in opposite directions for exactly 2

Question 143226: Hi, this is a question from the Math Review for the GRE General Test.
Two cars started from the same point and traveled on a straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 miles per hour faster than the other car, what was the average speed for each car for the 2-hour trip?

Thank you so much for the help,
Lauren
Answer by solver91311(12126) (Show Source):
You can put this solution on YOUR website!
Speed of one of the cars: r
Speed of the other car: r + 8

Since they are travelling in opposite directions, they are moving apart at the sum of their speeds. For example, if one car is going 50 mph east, and another car is going 60 mph west, then they are getting farther apart at a rate of 50 + 60 = 110 mph.

At the end of 2 hours they are 208 miles apart.

Distance equals rate times time, or , which can be written

So d for this problem is 208, t is 2, and r is r + (r + 8), so:

So the slower car is going 48 mph, and the faster car is going 8 mph faster, or 56 mph.

Check the answer:

In 2 hours, the slower car will have traveled 48 * 2 = 96 miles. The faster car will have traveled 56 * 2 = 112 miles. 112 plus 96 equals 208, answer checks.