Question 815344: [ Jill goes to work on a commuter train and travels 25 miles. She rides the train back home the same 25 miles. It takes an hour and 50 minutes round trip. The train ride home is 5 mph faster than the one taken to work. How fast are the trains going each way? ]
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! d = 25 miles
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w = going to work time
h = coming home time
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w + h = 60 + 50 = 110 minutes = 1.833333 hours
w = 1.833333 - h
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s = d / t
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speeds:
25/h = 25/w + 5
25/h - 25/w = 5
25w/hw - 25h/hw = 5
(25w - 25h)/hw = 5
25w - 25h = 5hw
25(1.833333 - h) - 25h = 5h(1.833333 - h)
45.833333 - 50h = 9.166666h - 5hh
5hh - 59.166666h + 45.833333 = 0
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the above quadratic equation is in standard form, with a=5, b=-59.166666, and c=45.833333
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to solve the quadratic equation, plug this:
5 -59.166666 45.833333
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the roots of the quadratic are:
10.999999
0.833333
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since we know that w + h = 1.833333 hours, only the second root (0.833333) makes sense as the value of h:
h = 0.833333 hours
w = 1.833333 - 0.833333 hours = 1 hour
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Answer:
going to work speed = 25/1 = 25 mph
coming home speed = 25/0.833333 = 30 mph
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