SOLUTION: it takes a freight train 3 hours more to travel 200 miles than it takes an express train to travel 120 miles. the express train is 20 mph faster than the freight train. find the ra
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Question 347212: it takes a freight train 3 hours more to travel 200 miles than it takes an express train to travel 120 miles. the express train is 20 mph faster than the freight train. find the rate of both trains Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! it takes a freight train 3 hours more to travel 200 miles than it takes an
express train to travel 120 miles.
the express train is 20 mph faster than the freight train.
find the rate of both trains
:
Let s = speed of the freight
then
(s+20) = speed of the express
:
Write a time equation, time = dist/speed
:
Freight time - express time = 3 hrs - = 3
:
multiply by s(s+20), results:
200(s+20) - 120s = 3s(s+20)
:
200s + 4000 - 120s = 3s^2 + 60s
:
80s + 4000 = 3s^2 + 60s
:
0 = 3s^2 + 60s - 80s - 4000
A quadratic equation
3s^2 - 20s - 4000 = 0
Factors to:
(3x + 100)(s - 40) = 0
the positive solution is what we want here:
s = 40 mph is the freight
then
40 + 20 = 60 mph is the express
:
:
Check solution by finding the travel time of each
200/40 = 5 hr
120/60 = 2 hr
-------------
differs: 3 hr
