Question 654872: An express train leaves Grand Central Station 1 h after a freight train leaves the same station. The express train is traveling 12 mph faster than the freight train. Find the rate at which each train is traveling if the express train overtakes the freight train in 5 h.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! An express train leaves Grand Central Station 1 h after a freight train leaves the same station.
The express train is traveling 12 mph faster than the freight train.
Find the rate at which each train is traveling if the express train overtakes the freight train in 5 h.
:
let s = speed of the freight
then
(s+12) = speed of the express
:
the travel time of the express given as 5 hrs,
then the travel time of the freight is 6 hrs. (Left one hr earlier)
:
When the express catches the freight, they will have traveled the same distance
Write a distance equation; dist = time * speed
:
6s = 5(s+12)
6s = 5s + 60
6s - 5s = 60
s = 60 mph is the speed of the freight
and
60+12 = 72 mph is the speed of the express
:
:
Check this by finding the actual dist of each, should be equal
Freight: 6(60) = 360 mi
Express: 5(72) = 360 mi
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