A passenger train leaves the train depot 2 hours after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of each train, if the passenger overtakes the freight train in 3 hours.

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- anonymous

- katieb

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- cathyangs

Ok so first of all, let's assign two variables, a and b, as the speeds (or rates) of each train.
But we do know that the freight train a is 20 less than the passenger, b.
so a=b-20.
We also know that a goes for 2 hours more than b. And the 2 extra hours plus the 3 hours is 5 hours that a was moving.
so 5 hours x a mph is the distance they were from the depot when they crossed paths.
And 3 hours x b mph is also that distance.
We have a formula from before that we can use instead of a.
so:
5 (b-20) is equal to 3b
5(b-20)=3b
Do you get it? Solve for b, and tell me what you get! :)

- anonymous

5b- 100 = 3b
2b=100
b=50

- cathyangs

yes! :) and then you can plug that back into a=b-20 to get...?

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## More answers

- anonymous

30

- anonymous

so 50 and 30 are the answers

- cathyangs

Yes, though you'd probably want to say it as 30 and 50, since that's the order the trains were mentioned. Good work! :)

- anonymous

ya thanks!

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