If the speed of boat in still water iss 9 mph and takes 1.5 miles to go and come 4 miles uptream and downward then the current of the river is 9.24 mph.
Given that the speed in still water be 9 mph, time to travel 4 miles upstream and downward is 1.5 hours.
We are required to find the speed of current of the river.
let the speed of current be c mph.
Effective speed in downstream=9+c
Effective speed in upstream=9-c
Total time=1.5 hours.
Total distance=4 miles.
Time for upstream stream+ time for downward stream=1.5 hours
2/(9+c)+2/(9-c)=1.5
18-2c+18+2c=1.5(9+c)(9-c)
36=1.5(81-[tex]c^{2}[/tex])
36=121.5-1.5[tex]c^{2}[/tex]
1.5[tex]c^{2}[/tex]=121.5-36
[tex]c^{2}[/tex]=85.5
c=9.24 mph.
Hence the speed of the current of the river is 9.24 mph.
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