By calculating the upstream and downstream distance and speed, the speed of the river is determined as 3mph.
It is given to us that -
Bob can row 9mph in still water.
The total time to travel downstream and return upstream to the starting point is 3 hours.
The total distance downstream and back is 24 miles
We have to find out the speed of the river (current speed).
Let us say x represent the speed of the river current.
This means that his total speed upstream = (9 - x) mph
This also means that his total speed downstream = (9 + x) mph.x
The total distance downstream and back is 24 miles.
This implies that -
The distance upstream = Distance downstream = 24/2 = 12 miles
We know that,
Time = Distance/speed
This implies, time taken to row upstream = 12/(9 - x)
and, time taken to row downstream = 12/(9 + x)
It is mentioned that total time to travel downstream and return upstream spent is 3 hours. This implies that -
12/(9 - x) + 12/(9 + x) = 3
=> 12(9 + x) + 12(9 - x) = 3(9 + x)(9 - x)
=> 108 + 12x + 108 - 12x = 3(81 - x²)
=> 216 = 3(81 - x²)
=> 216/3 = 81 - x²
=> 72 = 81 - x²
=> x² = 81 - 72 = 9
=> x =√9
=> x = 3
Thus, the speed of the river is 3 mph.
To learn more about upstream and downstream visit https://brainly.com/question/17300107
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