SOLUTION: A sailboat travels 20 milews downsteam in 3 hours. It returns in 4 hours. Find the speed of the sailboat in still water and the rate of the current.

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Question 168926: A sailboat travels 20 milews downsteam in 3 hours. It returns in 4 hours. Find the speed of the sailboat in still water and the rate of the current.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A sailboat travels 20 miles downstream in 3 hours. It returns in 4 hours. Find the speed of the sailboat in still water and the rate of the current.
:
A sailboat is a poor choice for writing these kind of problem since the speed is
dependent on the wind direction:
:
Anyway, ignoring that:
:
Let x = speed of boat in still water
Let y = speed of the current
then
(x-y) = speed upstream
(x+y) = speed downstream
:
Write two distance equations: Dist = time * speed
:
3(x + y) = 20; downstream
4(x - y) = 20; upstream
:
3x + 3y = 20
4x - 4y = 20
:
We wish to eliminate y: Multiply the 1st eq by 4, and the 2nd equation by 3:
12x + 12y = 80
12x - 12y = 60
---------------adding eliminates y
24x = 140
x =
x = 5 mph in still water
:
Find y:
3(5) + 3y = 20
:
17.5 + 3y = 20
3y = 20 - 17.5
3y = 2.5
y =
y = mph is the current
:
Check solution in the upstream equation:
4(5 - ) =
:
4(5) = 20 confirms out solutions