Question

A man can row 30 km upstream and 44 km downstream in 10 hours. Also, he can row 40 km upstream and 55 km downstream in 13 hours. The rate of the current is

• A. 3 km/hr
• B. 3.5 km/hr
• C. 4 km/hr
• D. 4.5 km/hr

Hint:

When solving speed, time, and distance problems, set up two equations, one for upstream and one for downstream, then solve the system of equations.

Answer 1

The Correct Option is A

Let the speed of the man in still water be \( x \) km/hr and the speed of the stream be \( y \) km/hr. We can write two equations based on the given conditions: - For the first case (30 km upstream and 44 km downstream in 10 hours): \[ \frac{30}{x - y} + \frac{44}{x + y} = 10 \quad \text{(i)} \] - For the second case (40 km upstream and 55 km downstream in 13 hours): \[ \frac{40}{x - y} + \frac{55}{x + y} = 13 \quad \text{(ii)} \] Solving equations (i) and (ii), we get: \[ x = 8 \text{ km/hr,} \quad y = 3 \text{ km/hr} \] Thus, the speed of the stream is \( 3 \) km/hr.