The speed of the river current if the speed of the motorboat in still water is 15 km/h is 3 km/h.
Let x be the speed of the current in km/h units
Speed of the boat traveling against the current= (15-x) km/h
Time spent traveling 36 miles against the current=36/15-x hours
Time spent rafting36miles (with the current) =35/x hours
Equation=36/x-36/15-x=9
Multiply both sides by x×(15-x)
36×(15-x) - 36x = 9x×(15-x)
540 - 36x - 36x=135x-9x²
9x²-207x+540=0
x²-23x+60=0
(x-3)×(x-30) = 0
Roots are x= 3 and x= 30
Since 15-x must be positive, the only root x = 3 survives
Hence:
Speed =3 km/h
Inconclusion the speed of the river current if the speed of the motorboat in still water is 15 km/h is 3 km/h.
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