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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?

cool

ant101  May 13, 2018
 #1
avatar+964 
+2

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
 #2
avatar+3282 
+2

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.

smileysmiley

tertre  May 13, 2018
 #3
avatar+591 
+1

Thanks so much!

ant101  May 13, 2018
 #4
avatar+964 
+1

No problem, glad I can help!

GYanggg  May 13, 2018

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