Question 179362: 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.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Use the basic formula that relates distance, rate, and time. 
Both of the trains travelled the same distance, namely 60 miles, so 
If we let the speed of the local train be r, and the express train travels twice as fast, the speed of the express train must be 2r.
If we let the elapsed time for the local train to make the trip be t, and the express train arrived two hours earlier, the elapsed time for the express train must be t - 2.
Now we can say, with respect to the local train's journey:  and with respect to the express train's journey: ) .
Since both of the right-hand expressions are equal to the same thing, namely 60, we can set them equal to each other:
 \rightarrow rt = 2rt - 4r \rightarrow -rt = -4r \rightarrow t = 4)
Telling us that the total time for the local train to make the 60 mile journey was 4 hours.
If then 
Therefore the speed of the local train is 15 mph. The speed of the express train is given as twice that, or 30 mph.
Hmm...I think I'll drive.
John
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