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. Therefore, the speed downstream is \( x + y \) km/h and the speed upstream is \( x - y \) km/h. Given: - Downstream distance = 24 km, Time = 3 hours - Upstream distance = 24 km, Time = 6 hours Using the formula Speed = Distance / Time:Downstream speed = \( \frac{24}{3} = 8 \) km/h. Upstream speed = \( \frac{24}{6} = 4 \) km/h. This yields the following system of equations:- \( x + y = 8 \) - \( x - y = 4 \) Adding the two equations:\[(x + y) + (x - y) = 8 + 4 \]\[2x = 12 \quad \Rightarrow \quad x = 6\] The speed of the boat in still water is 6 km/h. Answer: \(\boxed{6}\)