SOLUTION: An express and local train leave GraysLake 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 the local. Find

Algebra ->  Linear-equations -> SOLUTION: An express and local train leave GraysLake 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 the local. Find       Log On


   

Question 574570: An express and local train leave GraysLake 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 the local. Find the speed of each train.
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 GraysLake 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 the local.
Find the speed of each train.
:
let s = speed of the local
then
2s = speed of the express
:
write a time equation: time = dist/speed
:
Local time - Express time = 1 hr
50%2Fs - 50%2F%282s%29 = 1
Multiply by 2s
2s*50%2Fs - 2s*50%2F%282s%29 = 2s(1)
cancel the denominators
2(50) - 50 = 2s
100 - 50 = 2s
50 = 2s; 50 mph is the speed of express
and
s = 50/2 = 25 mph is the speed of the local
;
:
Check this by finding the time of each
Local: 50/25 = 2 hrs
Expre: 50/50 = 1 hr
--------------------
difference = 1 hr