• Feb 27th 2013, 09:06 PM
curt26
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!
• Feb 28th 2013, 01:01 AM
BobP
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.)
• Feb 28th 2013, 04:04 AM
pspss
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