SOLUTION: Engine pulls train 140 miles, 2nd engine is 5 mph faster than first, takes over and pull the train 200 miles, total time required for 6 hrs. find the average rate of each engin

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Question 356937: Engine pulls train 140 miles, 2nd engine is 5 mph faster than first, takes over and pull the train 200 miles, total time required for 6 hrs.
find the average rate of each engine.
totally stuck on the setup of the problem..
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Engine pulls train 140 miles,
2nd engine is 5 mph faster than first, takes over and pull the train 200 miles,
total time required for 6 hrs.
find the average rate of each engine.
:
Let s = speed of the slower engine
then
(s+5) = speed of the faster
:
Write a time equation, Time = dist/speed
:
Slow engine time + fast engine time = 6 hrs
140%2Fs + 200%2F%28%28s%2B5%29%29 = 6
multiply by s(s+5), results
140(s+5) + 200s = 6s(s+5)
:
140s + 700 + 200s = 6s^2 + 30s
Arrange as a quadratic on the right
0 = 6s^2 + 30s - 140s - 200s - 700
6s^2 - 310s - 700 = 0
Simplify, divide by 2
3s^2 - 155s - 350 = 0
Use the quadratic formula to find the positive solution
x+=+%28-%28-155%29+%2B-+sqrt%28-155%5E2-4%2A3%2A-350+%29%29%2F%282%2A3%29+
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