SOLUTION: Hamilton rode his bike downhill 12 miles on the river trail from his house to the ocean and then rode uphill to return home. His uphill speed was 6 miles per hour slower than his

Question 1168026: Hamilton rode his bike downhill 12 miles on the river trail from his house to the ocean
and then rode uphill to return home. His uphill speed was 6 miles per hour slower than
his downhill speed. It took him 3 hours longer to get home than it took him to get to the
ocean. Find Hamilton’s downhill speed and uphill speed.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
speed going is x mph and it took him 12/x hours to get there.
Speed returning is (x-6) mph and it took him 12/(x-6) hours to get home
(12/x)+3=12/(x-6) since 3 hours longer returning
multiply through by x(x-6)
12(x-6)+3x(x-6)=12x
12x-72 + 3x^2-18x=12x
12x disappear
3x^2-18x-72=0 divide by 3
x^2-6x-24=0
x=(1/2)(6+/- sqrt(36+96));sqrt 132=11.49
positive root is 8.745 mph
It took him 1.37 hours to get there at 8.745 mph and 4.37 hours to get home at 2.745 mph.

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