SOLUTION: The express train made the trip in 20 hours. The freight train took 25 hours because it was 10 miles per hour slower than the express train. What was the speed of each train?

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Question 1202491: The express train made the trip in 20 hours. The freight train took 25 hours because it was 10 miles per hour slower than the express train. What was the speed of each train?
Found 3 solutions by Theo, josgarithmetic, greenestamps:
Answer by Theo(13342) About Me  (Show Source):
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rate * time = distance
express train made the trip in 20 hours.
equation for express train is r * 20 = d
r is the rate
d is the distance
the freight train took 25 hours because it was 10 miles per hour slower than the exptress.
equation for freight train is (r - 10) * 25 = d
simplify the second equation and leave the first eqution as is to get:
r * 20 = d
r * 25 - 250 = d
subtract the first equation from the second to get:
5 * r - 250 = 0
add 250 to both sides of the equation the solve for r to get:
5 * r = 250 resulting in r = 50
this suggests that the express was traveling at 50 miles per hour and the freight train was traveling at 40 miles per hour.
equation become:
50 * 20 = d
40 * 25 = d
solve for d in both equaations to get d = 1000 in each equation.
solutuion is that the speed of the express train was 50 miles per hour and the speed of the freight train was 40 miles per hour.


Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
                   SPEED        TIME        DISTANCE
EXPRESS             r             20           d
FREIGHT             r-10          25           d

Each train, same distance d.
20r=25%28r-10%29

20r=25r-25%2A10
25r-20r=25%2A10
%2825-20%29r=25%2A10
highlight%28r=%2825%2A10%29%2F%2825-20%29%29

system%28EXPRESS%2CFREIGHT%29------system%28r=50%2Cr-10=40%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The distances are the same, and the ratio of the two times is 4:5, so the ratio of the two speeds is 5:4.

Simple reasoning says that, since the difference in the two speeds is 10 mph, the two speeds are 50 mph and 40 mph.

More formally, using the 5:4 ratio of the speeds....

Let 5x be the speed of the express train
Let 4x be the speed of the freight train

The express train is 10 mph faster than the freight train:

5x-4x=10
x=10

ANSWERS:
freight train speed = 4x = 40 mph
express train speed = 5x = 50 mph