OG - pg. 244 - #14

[angie]

Hello. I'm having trouble solving this problem:

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 of each car for the 2-hour trip?

Thanks in advance :D

[tommywallach]

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 of each car for the 2-hour trip?

Hey Angie,

This is a rates question, so we'll set up Rate * Time = Distance (as we do on EVERY rates question).

Rate * Time = Distance

Car A r 2 d
Car B r + 8 2 208 - d

Let's make sure we understand these pieces. One car went some rate, so we can call that r. The other car went 8mph faster, so we can call that r + 8.

The other tough piece is the distance. One car went some distance, so we can call that d. The other car had to go some distance such that the two cars together went 208 miles. Notice that d + (208 - d) = 208. So the two cars would always have gone 208 together.

Now multiply and solve:

First equation: 2r = d

Second Equation: 2 (r + 8) = 208 - d
2r + 16 = 208 - d

Now we can plug in "2r" for "d" in the second equation:

2r + 16 = 208 - 2r
4r = 192

r = 48

So one car went 48, and the other went 56.

Did that help?

-t