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# frog question

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A frog swims 8 miles downstream in 2 hours. She returns upstream in 14 hours. How fast does the frog swim in still water?

ant101  May 13, 2018
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Hey ant101!

x = speed of frog

y = speed of current

We use (distance)=(rate)*(time)

We can set up the system of equations:

$$(x+y)\cdot2=8\\ (x-y)\cdot14=8$$

Solving for x, we get:

$$x=\frac{16}7$$

I hope this helped,

Gavin

GYanggg  May 13, 2018
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The current helps the frog swim downstream and hinders her swimming upstream. Let the frog's rate in still water be $$x$$ and the current be $$y.$$ Thus, the swimming downstream the frog's rate is $$x+y$$ , while swimming upstream it is $$x-y$$ . Now apply rate times equals distance: downstream, we have

$$(x+y)(2)=8$$

and upstream gives

$$(x-y)(14)=8$$

Solving these equations, we find that $$(x,y)=(16/7, 12/7).$$

Thus the frog's rate in still water is $$\boxed{\frac{16}{7}}$$miles per hour.

tertre  May 13, 2018
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Thanks so much!

ant101  May 13, 2018
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No problem, glad I can help!

GYanggg  May 13, 2018