SOLUTION: 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, o

Question 118052: 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?
I set up two equations A and B being rates in MPH
equation 1-- multiplied times 2 to get it A and B in distances instead of rate.
equation 2-- set this equation to get the relationship between rates
Equation 1: 2A+2B=208
Equation 2: A=8+B
then solved by plugging Equation 2 into Equation 1
got B = 23 and A = 31
which according to my answer key is not right, it says 48 and 56. I am missing some stupid detail somewhere can you help me out. It doesn't matter which is A or B. Thanks a lot for your help

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=speed of first car, y=speed of second car

You're on the right track since you have the correct equations set up

Start with the given system

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute

Combine like terms on the left side

Subtract 16 from both sides

Combine like terms on the right side

Divide both sides by 4 to isolate y

Divide

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So our answer is and

So the first car was going 56 mph and the second car was going 48 mph
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