<PRE><B>Question 148931</B>
n express and local train leave Gray&#39;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.
:
The time they left is irrelevant to the problem
:
Let s = speed of the local
then
2s = speed of the express
:
Write a time equation: Time = {{{dist/speed}}}
:
Express time + 1 hr = Local time
{{{50/(2s)}}} + 1 = {{{50/s}}}
Get rid of the denominators, mult equation by 2s; results:
50 + 2s = 2(50)
2s = 100 - 50
2s = 50
s = {{{50/2}}}
s = 25 mph speed of the local
then
50 mph speed of the express
;
;
Check solution
{{{50/50}}} + 1 = {{{50/25}}}
1 + 1 = 2 </PRE>