The correct answer is option (D):
3kmph
Let's break down this river flow problem. The key is understanding how the current affects the boat's speed.
* Upstream: When the boat travels against the current, the current slows it down.
* Downstream: When the boat travels with the current, the current speeds it up.
Let's use variables:
* Let 'x' be the speed of the river flow (in km/hr).
* The boat's speed in still water is 10 km/hr.
Therefore:
* Speed downstream (with the current) = 10 + x km/hr
* Speed upstream (against the current) = 10 - x km/hr
We know that Distance = Speed x Time, therefore Time = Distance / Speed.
* Time taken to travel downstream (91 km) = 91 / (10 + x) hours
* Time taken to travel upstream (91 km) = 91 / (10 - x) hours
The total time for the round trip is 20 hours. So:
91 / (10 + x) + 91 / (10 - x) = 20
To solve for 'x', we first need to get rid of the fractions. Multiply both sides of the equation by (10 + x)(10 - x):
91(10 - x) + 91(10 + x) = 20(10 + x)(10 - x)
Expanding the equation gives:
910 - 91x + 910 + 91x = 20(100 - x^2)
Simplifying:
1820 = 2000 - 20x^2
Rearranging:
20x^2 = 180
Dividing by 20:
x^2 = 9
Taking the square root of both sides:
x = 3 (We only consider the positive solution since speed cannot be negative).
Therefore, the speed of the flow of the river is 3 km/hr. This matches the correct answer.