Thread: Please help me solve this math word problem!

It takes a freight train 2 hours longer to travel 300 miles than it takes an express train to travel 280 miles. The rate of the express train is 20 miles per hour greater than the rate of the freight train. Find the times and rates of both trains.

Any help in the right direction would be appreciated. Thanks!

Start by giving each of the unknowns a name, say,
FS = speed of the freight train, FT the time for its journey.
ES = speed of the express train, ET the time for its journey.
Choose other letters or names if you prefer, but it helps if you can choose names suggestive of what they represent.

Put the information that you are given in terms of your chosen names.

So,
FT = 300/FS,
ET = 280/ES,
FT - ET = 2, etc.

Having done that, solve the equations.
(Doing that gets you to a quadratic, but that does factorize easily.)

Let freight train speed be x mile/hr
and that of express train = (x + 20) mph
300/x – 300/(x + 20) = 2
300x + 6000 – 300x = 2x(x + 20)
2x^2 + 40x – 6000 = 0
x^2 + 20x – 3000 = 0

using quadratic formula
x = 45.67 taking +ve values of freight train
(x + 20 = 65.67 of express train
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Thank you so much for the help! I appreciate it. Pspss I'm assuming you accidentally put 300 in for the express train distance instead of 280?

Thanks again