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
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