SOLUTION: 2. An express train and a local train both leave Gray�s Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ah

Question 199079: 2. An express train and a local train both leave Gray�s Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ahead of it. Find the speed of each train.

I am confused by this problem and do not know where to start.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let = time of express train and = time of local train

Also, let = speed of express train and = speed of local train

Since the "express train travels twice as fast as the local train", this means that

Also, because "the express train arrives 2 hours ahead of the local train", this tells us

Now let's set up the formula for the local train:

Start with the distance rate time formula

Plug in , and

Divide both sides by .

So after isolating the second speed, we get

Now let's set up the formula for the express train:

Start with the distance rate time formula

Plug in , and

Plug in and

Plug in

Multiply

Multiply both sides by .

Distribute

Subtract from both sides.

Combine like terms.

Divide both sides by -60 to isolate .

Divide

So it takes 4 hours for the local train

Go back to the local train formula

Plug in

Divide both sides by 4.

Divide.

So the speed of the local train is 15 mph

Now simply double the speed of the local train to get

So the speed of the local train is 15 mph and the speed of the express train is 30 mph.

Note: nowhere in the solution above is a mention of 12:00 noon. This information is unnecessary and it is put in there to throw you off.
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