a motorboat traveled a distance of 72 miles in 3 hours while

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!

Solution

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