SOLUTION: Margie walks 3 miles to the park and returns home on roller skates. Her roller skating speed is 4 miles per hour faster than her walking speed.The total round-trip time is 2 hours.

Question 1042053: Margie walks 3 miles to the park and returns home on roller skates. Her roller skating speed is 4 miles per hour faster than her walking speed.The total round-trip time is 2 hours. Find Margie's skating speed in miles per hour.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Margie walks 3 miles to the park and returns home on roller skates.
Her roller skating speed is 4 miles per hour faster than her walking speed.
The total round-trip time is 2 hours.
Find Margie's skating speed in miles per hour.
:
Let s = the walking speed
then
(s+4) = the skating speed
:
Write a time equation; time = dist/speed
to park time + return time = 2hrs
+ = 2
multiply equation by s(s+4), cancel the denominators
3(s+4) + 3s = 2s(s+4)
3s + 12 + 3s = 2s^2 + 8s
Arrange as a quadratic equation on the right
0 = 2s^2 + 8s - 6s - 12
2s^2 + 2s - 12 = 0
simplify divide by 2
s^2 + s - 6 = 0
Factors to
(s+3)(s-2) = 0
the positive solution is what we want here
s = 2 mph is the walking speed
Therefore
2 + 4 = 6 mph is the skating speed
:
:
See if this checks out find actual time each way
3/2 = 1.5 hrs
3/6 = .5 hrs
---------------
total time 2 hrs

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