Question 113024: can anyone help with this?: a motorboat traveled a distance of 72 miles in 3 hours while traveling with the current. Against the curtrent the same trip took 4.5 hours. find the rate of the motorboat in calm water and the rate of the current.thanks so much!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a motorboat traveled a distance of 72 miles in 3 hours while traveling with the current. Against the current the same trip took 4.5 hours. find the rate of the motorboat in calm water and the rate of the current.thanks so much!
:
Let x = speed of the boat in still water
and
Let y = speed of the current
Then:
(x+y) = actual speed down-stream
and
(x-y) = speed up-stream
:
Write two distance equations. Dist = time * speed:
:
Downstream: 3(x + y) = 72
Upstream: 4.5(x - y) = 72
:
WE can simplify both of these equations:
Divide the 1st equation by 3, and the 2nd equation by 4.5, you then have:
:
x + y = 24
x - y = 16
-------------adding eliminates y, find x
2x +0 = 40
x = 40/2
x = 20 mph speed of the boat in still water
:
Use x + y = 24 to find y
20 + y = 24
y = 24 - 20
y = 4 mph; speed of the current
:
:
Check solutions in the original upstream equation:
4.5(20 - 4) =
4.5 * 16 = 72; confirms our solutions
:
How about this? Did it make sense to you? Any questions?
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