Question

A boat which can travel at 10km/hr in still water goes 91km down a river and returns to the starting point in 20 hours. Find the speed of the flow of the river.

• A. 3.5kmph
• B. 2.5kimph
• C. 2kmph
• D. 3kmph
• E. 4 kmph

Answer 1

The Correct Option is D

Step 1: Understand the problem.
The boat can travel at 10 km/h in still water. The boat travels 91 km down the river and then returns to the starting point. The total time taken for the round trip is 20 hours. We are asked to find the speed of the flow of the river.

Step 2: Define variables.
Let the speed of the flow of the river be \( x \) km/h.
- When the boat is going downstream (with the flow), its effective speed is \( 10 + x \) km/h.
- When the boat is going upstream (against the flow), its effective speed is \( 10 - x \) km/h.

Step 3: Calculate the time taken for each part of the journey.
- Time taken to go downstream: \( \frac{91}{10 + x} \) hours.
- Time taken to go upstream: \( \frac{91}{10 - x} \) hours.
The total time for the round trip is 20 hours, so:
\( \frac{91}{10 + x} + \frac{91}{10 - x} = 20 \)

Step 4: Solve the equation.
Multiply both sides of the equation by \( (10 + x)(10 - x) \) to eliminate the denominators:
\( 91(10 - x) + 91(10 + x) = 20(10^2 - x^2) \)
\( 91(10 - x + 10 + x) = 20(100 - x^2) \)
\( 91(20) = 20(100 - x^2) \)
\( 1820 = 2000 - 20x^2 \)
\( 20x^2 = 2000 - 1820 \)
\( 20x^2 = 180 \)
\( x^2 = \frac{180}{20} = 9 \)
\( x = 3 \)

Step 5: Conclusion.
The speed of the flow of the river is 3 km/h.

Final Answer:
The correct option is (D): 3 km/h.