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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On


   

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) About Me  (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
2x%2B2y=208
x=8%2By



2%288%2By%29%2B2y=208 Plug in x=8%2By into the first equation. In other words, replace each x with 8%2By. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


16%2B2y%2B2y=208 Distribute


4y%2B16=208 Combine like terms on the left side


4y=208-16Subtract 16 from both sides


4y=192 Combine like terms on the right side


y=%28192%29%2F%284%29 Divide both sides by 4 to isolate y



y=48 Divide




Now that we know that y=48, we can plug this into x=8%2By to find x



x=8%2B%2848%29 Substitute 48 for each y


x=56 Simplify


So our answer is x=56 and y=48


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