Mathematics: Raft 16 miles with river current.at end of 16 miles turns around and rafts against river current. overall the journey takes 4 hours he can raft 9 mph in still water. what is speed of current

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Raft 16 miles with river current.at end of 16 miles

lydiaa1

08.01.2022

Let the speed of the current of the river be = x

And, the speed of the boat in still water = 9 mph

Then, the speed of boat along the river current will be= 9+x mph

And, speed of boat against the river current will be = 9-x mph

Now as given, total distance along river current and total distance against river current is same = 16 miles.

As we know, time=distance/speed

Time taken by boat along the river current = $\frac{16}{9+x}$

And time taken by boat against the river current = $\frac{16}{9-x}$

Also given is , the overall the journey takes 4 hours; so equation becomes

$\frac{16}{9+x}+\frac{16}{9-x}=4$

$4(\frac{1}{9+x}+\frac{1}{9-x})=1$

Solving this we get; $x^{2} =9$ or x=3

Therefore, the speed of the current of the river is 3 mph.

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