Question

A man can row 24 km downstream in 3 hours and the same distance upstream in 6 hours. What is the speed of the boat in still water?

• A. 4 km/h
• B. 5 km/h
• C. 6 km/h
• D. 8 km/h

Hint:

To find the speed of the boat in still water, solve for \( x \) by adding and subtracting the downstream and upstream speed equations.

Answer 1

The Correct Option is B

Let the speed of the boat in still water be \( x \) km/h, and the speed of the stream be \( y \) km/h. - Speed downstream = \( x + y \) km/h - Speed upstream = \( x - y \) km/h Given: - Distance downstream = 24 km, Time = 3 hours - Distance upstream = 24 km, Time = 6 hours Using the formula: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] Downstream speed = \( \frac{24}{3} = 8 \) km/h, Upstream speed = \( \frac{24}{6} = 4 \) km/h. Now, we have the equations: - \( x + y = 8 \) - \( x - y = 4 \) Adding these two equations: \[ (x + y) + (x - y) = 8 + 4 \] \[ 2x = 12 \quad \Rightarrow \quad x = 6 \] Thus, the speed of the boat in still water is 6 km/h. Answer: \(\boxed{6}\)