SOLUTION: Hi, How would I solve the following: Applications of Linear Equations An express and local train leave Gray’s Lake at 3 P.M. and head for Chicago 50 miles away. The express

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Question 152521: Hi,
How would I solve the following: Applications of Linear Equations
An express and local train leave Gray’s Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the speed of each train.
Thank you so much for your help.
Sally
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate times time equals distance.
The express train travels at a rate of R%5Be%5D and takes t%5Be%5D to travel the 50 miles.
1.R%5Be%5D%2At%5Be%5D=50
The local train travels at a rate of R%5Bl%5D and takes t%5Bl%5D to travel the 50 miles.
2.R%5Bl%5D%2At%5Bl%5D=50
You also know that the rate of the express train is twice the rate of the local train.
R%5Be%5D=2%2AR%5Bl%5D
And finally you know that the local train arrived 1 hour after the express train.
t%5Bl%5D=t%5Be%5D%2B1
From 2,
2.R%5Bl%5D%2At%5Bl%5D=50
Substitute for R%5Bl%5D and t%5Bl%5D
2.R%5Bl%5D%2At%5Bl%5D=50
%281%2F2%29%2AR%5Be%5D%2A%28t%5Be%5D%2B1%29=50
R%5Be%5D%2A%28t%5Be%5D%2B1%29=100
R%5Be%5D%2At%5Be%5D%2BR%5Be%5D=100
From 1, you know that R%5Be%5D%2At%5Be%5D=50
R%5Be%5D%2At%5Be%5D%2BR%5Be%5D=100
50%2BR%5Be%5D=100
R%5Be%5D=50
The express train travels at 50 miles per hour.
From 1,
R%5Be%5D%2At%5Be%5D=50
50%2At%5Be%5D=50
t%5Be%5D=1
The express train takes 1 hour to reach Chicago.
R%5Be%5D=2%2AR%5Bl%5D
50=2%2AR%5Bl%5D
R%5Bl%5D=25
The local train travels 25 miles per hour.
t%5Bl%5D=t%5Be%5D%2B1
t%5Bl%5D=1%2B1
t%5Bl%5D=2
The local train takes 2 hours to reach Chicago.