SOLUTION: John's speed on his drive to work in the morning averages 15mph faster then his speed on the return trip in the evening on the same route. His driving time in the morning is 15 mi

Question 586421: John's speed on his drive to work in the morning averages 15mph faster then his speed on the return trip in the evening on the same route. His driving time in the morning is 15 minutes less than his driving time in the evening. What are his speeds to and from work? What are his drving times? The distance from home to work is 25 miles.
I dont know how to proceed with this, I think it might be too wordy! Thank you for any help.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
John's speed on his drive to work in the morning averages 15mph faster then his speed on the return trip in the evening on the same route.
His driving time in the morning is 15 minutes less than his driving time in the evening.
What are his speeds to and from work?
What are his drving times?
The distance from home to work is 25 miles.
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From work DATA:
distance = 25 miles ; rate = x mph ; time = d/r = 25/x hrs
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To work DATA:
distance = 25 miles ; rate = x+15 mph ; time = d/r = 25/(x+15) hrs
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Equation:
from work time - to work time = 1/4 hr
----
25/x - 25/(x+15) = 1/4
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Divide thru by 25 to get:
1/x - 1/(x+15) = 1/100
--------
100(x+15) - 100x = x(x+15)
1500 = x^2+15x
x^2+15x-1500 = 0
I graphed the quadratic and got
x = 31.95 mph (from work time)
x+15 = 46.95 mph (to work time)
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Cheers,
Stan H.
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