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Sherry drove 168 miles from her hometown to the city.
During her return trip, she was able to increase her speed by 14 mph.
If her return trip took 2 hours less time, find her original speed and speed returning home.
Let s = speed to the city
(s+14) = speed home
Write a time equation, time = dist/speed
To city time - return time = 2 hrs
Multiply by s(s+14), results:
168(s+14) - 168s = 2s(s+14)
168s + 2352 - 168s = 2s^2 + 28s
A quadratic equation
2s^2 + 28s - 2352 = 0
Simplify divide by 2
s^2 + 14s - 1176 = 0
You can use the quadratic formula, a=1, b=14, c=-1176, but this will factor to:
(s+42)(s-28) = 0
The positive solution
s = 28 mph to the city
28+14 = 42 mph return home
Check this by finding the times
168/28 = 6 hrs
168/42 = 4 hrs
differs: 2 hrs; confirms our solutions