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A motorboat maintained a constant speed of 20 miles per hour relative to the water in going 21 miles upstream and then returning. The total time for the trip was 2.5 hours. Use this information to find the speed of the current.

 Mar 23, 2021
 #1
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Let  the speed  of the current  be  = R

Speed with current  = 20 + R

Speed  against current = 20 - R

 

And.......  Distance /  Rate   Time

 

So

 

21  /  (20 + R)  +  21 / ( 20 - R)  = 2.5     simplify

 

21 ( 20 - R) + 21(20 + R)  =  2.5 ( 20 + R) (20 - R)

 

420  + 420  =  2.5 ( 400 - R^2)

 

840 =  2.5 (400 - R^2)      divide both sides by  2.5

 

336   =  400  - R^2

 

R^2  =  400 -  336

 

R^2  =  64       take  the positive root

 

R = sqrt (64)  =   8 ( mph)

 

 

cool cool cool

 Mar 23, 2021

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