SOLUTION: A motorboat heads upstream a distance of 24 miles on a river whose current is running at 3 miles per hour. The motorboat then returns to the original place heading downstream. The
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Question 1020566: A motorboat heads upstream a distance of 24 miles on a river whose current is running at 3 miles per hour. The motorboat then returns to the original place heading downstream. The total trip up and back takes 6 hours. What was the speed of the motorboat assuming it maintained a constant speed? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A motorboat heads upstream a distance of 24 miles on a river whose current is running at 3 miles per hour.
The motorboat then returns to the original place heading downstream.
The total trip up and back takes 6 hours.
What was the speed of the motorboat assuming it maintained a constant speed?
:
let s = the speed of the boat in still water
then
(s-3) = effective speed upstream
and
(s+3) = effective speed downstream
:
Write a time equation; time = dist/speed
:
Time up + time down = 6 hrs + = 6
:
Multiply equation by (s-3)(s+3), cancel the denominators and you have
24(s+3) + 24(s-3) = 6(s-3)(s+3)
24s + 72 + 24s - 72 = 6(s^2 - 9)
48s = 6s^2 - 54
A quadratic equation
0 = 6s^2 - 48s - 54
Simplify, divide by 6
s^2 - 8s - 9 = 0
Factors to
(s - 9) (s + 1) = 0
the positive solution
s = 9 mph the speed of the boat in still water
:
:
:
Check this, find the time each way
24/6 = 4 hrs upstream
24/12 = 2 hrs down
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total: 6 hrs
