SOLUTION: Roma 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

Question 472436: Roma 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.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
then
(s+14) = speed home
:
Write a time equation, time = dist/speed
:
To city time - return time = 2 hrs
- = 2
:
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
then
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
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