Question

A motor boat covers a certain distance downstream in 30 minutes, while it comes back in 45 minutes. If the speed of the stream is 5 kmph, what is the speed of the boat in still water?

• A. 10 kmph
• B. 15 kmph
• C. 20 kmph
• D. 25 kmph
• E.

Hint:

For problems involving downstream and upstream travel, use the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}}, \] and set up an equation to solve for the unknown speed in still water.

Answer 1

The Correct Option is D

1. Define variables: - Let the speed of the boat in still water be \( b \) kmph. - The speed of the stream is \( 5 \) kmph. 2. Calculate downstream speed: \[ \text{Downstream speed} = b + 5 \text{ kmph} \] 3. Calculate upstream speed: \[ \text{Upstream speed} = b - 5 \text{ kmph} \] 4. Define distance relation: - Since the distance covered downstream and upstream is the same, let it be \( D \). 5. Compute time taken downstream: \[ \text{Time downstream} = 30 \text{ minutes} = 0.5 \text{ hours} \] Using the distance formula: \[ D = (b + 5) \times 0.5 \] 6. Compute time taken upstream: \[ \text{Time upstream} = 45 \text{ minutes} = 0.75 \text{ hours} \] Using the distance formula: \[ D = (b - 5) \times 0.75 \] 7. Set the two expressions for \( D \) equal to each other: \[ (b + 5) \times 0.5 = (b - 5) \times 0.75 \] 8. Solve for \( b \): \[ 0.5b + 2.5 = 0.75b - 3.75 \] \[ 2.5 + 3.75 = 0.75b - 0.5b \] \[ 6.25 = 0.25b \] \[ b = \frac{6.25}{0.25} = 25 \text{ kmph} \] Final Answer: The speed of the boat in still water is \boxed{25 \text{ kmph}}.