a paddle boat can move at a speed of 18km/h in still water. the boat is paddled 12km downstream in a river in the same time it takes to go 6km upstream. what is the speed of the river?

Question

mertsj · Answer

distance divided by rate = time.  The upstream time is equal to the downstream time.  The upstream rate is the still water rate - the rate of the current.  The downstream rate is the still water rate + the rate of the current.

e.mccormick · Answer

These are all about the setup.  Because the need result is the same, you can do these as a ratio.

Because the 18 is the known speed and the unknown x is the river speed, we can say that going down is (18+x) and up is (18-x).  Downstream you add the river, up (against) you subtract.  That makes those one part of the ratio, both bottom for instance.

Now, you are given known distances at this speed of 6 and 12.  These would be other other parts.  So the end result is solving:

$$\frac{6}{(18-x)}=\frac{12}{(18+x)}$$

mertsj · Answer

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