SOLUTION: A ferry boat takes people up and down the river 40 miles between two towns. The boat travels downstream in 3/5 the time it takes to travel upstream. If the ferry boat can travel at

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Question 765239: A ferry boat takes people up and down the river 40 miles between two towns. The boat travels downstream in 3/5 the time it takes to travel upstream. If the ferry boat can travel at 12 mph in still water, how fast is the current of the river? How fast does the boat travel upstream? Downstream?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A ferry boat takes people up and down the river 40 miles between
two towns.
The boat travels downstream in 3/5 the time it takes to travel upstream.
If the ferry boat can travel at 12 mph in still water, how fast is the
current of the river?
How fast does the boat travel upstream? Downstream?
:
let c = the rate of the current
then
(12-c) = speed upstream
and
(12+c) = speed downstream
:
Time downstream = 3/5 the time upstream
3/5 = .6
write a time equation; time = dist/speed
.6(40%2F%28%2812-c%29%29) = 40%2F%28%2812%2Bc%29%29
which is
24%2F%28%2812-c%29%29 = 40%2F%28%2812%2Bc%29%29
cross multiply
24(12+c) = 40(12-c)
288 + 24c = 480 - 40c
24c + 40c = 480 - 288
64c = 192
c = 192/64
c = 3 mph is current
therefore
12-3 = 9 mph upstream
and
12 + 3 = 15 mph down stream
:
:
Check this by finding the times
40/9 = 4.444
40/15 = 2.666
:
2.666/4.444 = .6 which is 3/5