word problem?

Question

The speed of a freight train is 10 miles per hour slower than the speed of a passenger train. The freight train travels 390 miles in the same time that it takes the passenger train to travel 480 miles. Find the speed of the freight train.
Give a numeric answer only, rounded to the nearst tenth of a mph. Although you may also find the speed of the passenger train, do not include that information with your response.

Answer 1

The key here is to turn these sentences into equations.

Let X be the speed of the freight train and Y the speed of the passenger train. Then the first equation we get is:

X = Y - 10

The next sentence tells us that in some set amount of time one train goes 390 miles while the other goes 480. There are two ways we can find our answer now.

1. We can notice that one train goes 90 miles further than the other. SInce it goes 10 miles per hour faster -- the trains must have been going for nine hours. That means that the freight train goes 390 miles in nine hours -- so it goes 43.3 MPH.

2. The other way is to note that 390/X = 480/Y. A little algebra gives us:

390Y = 480X

since X = Y-10, we get

390(X+10) = 480X

3900 = 90X

X = 43.3