SOLUTION: [ 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

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
---
the roots of the quadratic are:
10.999999
0.833333
---
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
---
Answer:
going to work speed = 25/1 = 25 mph
coming home speed = 25/0.833333 = 30 mph
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Solve and graph linear equations:
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---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Convert fractions, decimals, and percents:
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---
Calculate and graph the linear regression of any data set:
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