<PRE><B>Question 574570</B>
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/s}}} - {{{50/(2s)}}} = 1
Multiply by 2s
2s*{{{50/s}}} - 2s*{{{50/(2s)}}} = 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</PRE>