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A cabin cruiser traveling with the current went 12 mi in 1 h. Traveling against the current, it took 2 h to go the same distance. Find the rate of the cabin cruiser in calm water and the rate of the current

 Feb 17, 2020
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Call the rate of the  current, C

 

Call the rate of the  boat in still water, R

 

And with the  current, the boat travels at a rate of  R + C  mph

 

And against the  current the boat traravels at a rate of  R - C   mph

 

Rmember that  Distance / Rate  =   Time

 

And   time it took to travel  12 against the  current =  1 hour more than with the  current =  2 hours....so.....

 

12/ [ R + C ]  =  1        multiply both sides  by  R +  C

 

12 = R + C  →       12 - R  = C   (1)

 

And against  the current we have that

 

12/ ( R - C )  = 2     

 

12 = 2(R - C)                 divide through by 2  and sub (1)  in for  C

 

6 = R - (12 - R)          

 

6 = 2R- 12           

 

18 = 2R                    divide  both sides  by  2

 

9  (mph) =  R =   rate in still water

 

And the rate of the  current is   12 - 9 =  3 mph

 

 

cool cool cool

 Feb 17, 2020

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