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 152486: 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.
K.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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.
;
Let s = speed of the local train
then
2s = speed of the express
:
Write a time equation: Time = dist%2Fspeed
:
Local time - express time = 1 hr
50%2Fs - 50%2F%282s%29 = 1
Multiply equation by 2s to get rid of the denominators
2s*50%2Fs - 2s*50%2F%282s%29 = 2s(1)
Results
2(50) - 50 = 2s
:
100 - 50 = 2s
s = 50%2F2
s = 25 mph speed of the local, obviously, 50 mph is speed of express
:
:
Check solution in our time equation:
50%2F25 - 50%2F%2850%29 = 1
2 - 1 = 1
:
:
Pretty easy, right?