SOLUTION: How many minutes will a car traveling at 52 miles per hour take to catch up with a car traveling at 42 miles per hour if the slower car started two hours before the faster car?

Question 295219: How many minutes will a car traveling at 52 miles per hour take to catch up with a car traveling at 42 miles per hour if the slower car started two hours before the faster car?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
This is a two part question.
first you can find the distance traveled by the car in 2 hours
second how long will it take the second car to catch it.
Or we can put it all in two equations and solve simultaneously.
Let's do both and compare.
in 2 hours the slow car can go 2*42=84 miles.
the faster car will gain on the slow car at 52-42 =10 miles an hour.
so it will take the faster car 84/10 =8.4 hours to catch up.
the faster car goes x hours at 52 mph
the slower car goes (x+2) hours at 42 mph
they will go the same distance so we set them equal
42(x+2)=52x
42x+84=52x
84=10x
84/10=x
8.4 hours = x
same results
but now you see why and how the equation works.

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