SOLUTION: An express and local train leave Grayslake at 3pm 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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: An express and local train leave Grayslake at 3pm 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      Log On


   

Question 230819: An express and local train leave Grayslake at 3pm 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 josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = the speed of the local in mi/hr
Then 2s = speed of the express
Let t = time in hrs it takes for local to arrive in Chicago
Then t+-+1 time in hrs for express to arrive in Chicago
They both travel the same distance, d+=+50 mi
Now I can write an equation for each train
For local:
(1) 50+=+st
For express:
(2) 50+=+2s%2A%28t+-+1%29
---------------------
From (2)
50+=+2st+-+2s
Substitute from (1)
50+=+2%2A50+-+2s
2s+=+100+-+50
2s+=+50
s+=+25
and
2s+=+50
The speed of the local is 25 mi/hr and
the speed of the express is 50 mi/hr
check answer:
(1) 50+=+st
50+=+25t
t+=+2
(2) 50+=+2s%2A%28t+-+1%29
50+=+2%2A25%2A%282-1%29
50+=+50%2A1
50+=+50
OK