SOLUTION: 2. 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 t

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Question 164453: 2. 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.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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 = local train speed
then
2s = express train speed
:
Write a time equation: Time = dist%2Fspeed
:
Freight time = Express time + 1 hr
50%2Fs = 50%2F%282s%29 + 1
Multiply equation by 2s to get rid of the denominators
2(50) = 50 + 2s
100 - 50 = 2s
:
s = 50%2F2
s = 25 mph is the freight speed, obviously 50 mph is the express speed
:
:
Check solution by find the time of each
50/25 = 2 hr
50/50 = 1 hr, (1 hr less than the freight