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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let t%5B1%5D = time of express train and t%5B2%5D = time of local train

Also, let r%5B1%5D = speed of express train and r%5B2%5D = speed of local train


Since the "express train travels twice as fast as the local train", this means that r%5B1%5D=2%2Ar%5B2%5D


Also, because "the express train arrives 2 hours ahead of the local train", this tells us t%5B1%5D=t%5B2%5D-2



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


d=rt Start with the distance rate time formula


60=r%5B2%5D%2At%5B2%5D Plug in d=60, r=r%5B2%5D and t=t%5B2%5D


60%2Ft%5B2%5D=r%5B2%5D Divide both sides by t%5B2%5D.


So after isolating the second speed, we get r%5B2%5D=60%2Ft%5B2%5D



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


d=rt Start with the distance rate time formula


60=r%5B1%5D%2At%5B1%5D Plug in d=60, r=r%5B1%5D and t=t%5B1%5D


60=%282%2Ar%5B2%5D%29%2A%28t%5B2%5D-2%29 Plug in r%5B1%5D=2%2Ar%5B2%5D and t%5B1%5D=t%5B2%5D-2


60=%282%2A%2860%2Ft%5B2%5D%29%29%2A%28t%5B2%5D-2%29 Plug in r%5B2%5D=60%2Ft%5B2%5D


60=%28120%2Ft%5B2%5D%29%2A%28t%5B2%5D-2%29 Multiply


60t%5B2%5D=120%28t%5B2%5D-2%29 Multiply both sides by t%5B2%5D.


60t%5B2%5D=120t%5B2%5D-240 Distribute


60t%5B2%5D-120t%5B2%5D=-240 Subtract 120t%5B2%5D from both sides.


-60t%5B2%5D=-240 Combine like terms.


t%5B2%5D=-240%2F%28-60%29 Divide both sides by -60 to isolate t%5B2%5D.


t%5B2%5D=4 Divide


So it takes 4 hours for the local train


60=r%5B2%5D%2At%5B2%5D Go back to the local train formula


60=r%5B2%5D%2A4 Plug in t%5B2%5D=4


60%2F4=r%5B2%5D Divide both sides by 4.


15=r%5B2%5D Divide.


So the speed of the local train is 15 mph

Now simply double the speed of the local train to get 15%2A2=30

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.