SOLUTION: A passenger train traveled 100 miles in the same amount of time it took a fright train to travel 80 miles. The rate of the freight was 5 miles per hour slower than the rate of the

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: A passenger train traveled 100 miles in the same amount of time it took a fright train to travel 80 miles. The rate of the freight was 5 miles per hour slower than the rate of the       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1047445: A passenger train traveled 100 miles in the same amount of time it took a fright train to travel 80 miles. The rate of the freight was 5 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for both trains
Let +s+ = speed of the passenger train in mi/hr
+s+-+5+ = speed of the freight train in mi/hr
---------------------
Equation for passenger train:
(1) +100+=+s%2At+
Equation for freight train:
(2) +80+=+%28+s+-+5+%29%2At+
------------------------
(1) +t+=+100%2Fs+
and
(2) +80+=+%28+s-5+%29%2A%28+100%2Fs+%29+
(2) +80s+=+100s+-+500+
(2) +20s+=+500+
(2) +s+=+25+ mi/hr
and
+s+-+5+=+20+
The rate of the passenger train is 25 mi/hr
---------------
check:
(1) +100+=+s%2At+
(1) +100+=+25%2At+
(1) +t+=+4+ hrs
and
(2) +80+=+%28+s+-+5+%29%2At+
(2) +80+=+%28+25+-+5+%29%2At+
(2) +80+=+20t+
(2) +t+=+4+ hrs
OK

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

A passenger train traveled 100 miles in the same amount of time it took a fright train to travel 80 miles. The rate of the freight was 5 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train
Let rate of passenger train be S
Then rate of freight train is: S - 5
We then get the following TIME equation: 100%2FS+=+80%2F%28S+-+5%29
100(S - 5) = 80S ------ Cross-multiplying
100S - 500 = 80S
100S - 80S = 500
20S = 500
S, or rate of passenger train was: 500%2F20, or highlight_green%28matrix%281%2C2%2C+25%2C+mph%29%29