Question

A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. What is the speed of the river current in km/hr?

• A. 2
• B. 1
• C. 3
• D. 2.5

Hint:

- Use the formula for speed, distance, and time to set up equations and solve for the unknowns in current and boat speed problems.

Answer 1

The Correct Option is B

Step 1: Understanding the Problem
Let the speed of the boat in still water be \( b \) km/hr and the speed of the river current be \( c \) km/hr.
When the boat is rowing downstream, the effective speed of the boat is \( b + c \).
When the boat is rowing upstream, the effective speed of the boat is \( b - c \).
Step 2: Calculating Downstream and Upstream Speeds
Downstream: The man covers 15 km in 3 hours 45 minutes (which is \( 3.75 \) hours).
So, the effective downstream speed is: \[ \text{Speed downstream} = \frac{15}{3.75} = 4 \, \text{km/hr} \] Hence, \( b + c = 4 \). Upstream: The man covers 5 km in 2 hours 30 minutes (which is \( 2.5 \) hours).
So, the effective upstream speed is: \[ \text{Speed upstream} = \frac{5}{2.5} = 2 \, \text{km/hr} \] Hence, \( b - c = 2 \). Step 3: Solving the System of Equations
We now have the following system of equations: \[ b + c = 4
b - c = 2 \] Adding these two equations: \[ (b + c) + (b - c) = 4 + 2
2b = 6
b = 3 \] Substitute \( b = 3 \) into either equation, say \( b + c = 4 \): \[ 3 + c = 4
c = 1 \] Thus, the speed of the river current is \( c = 1 \, \text{km/hr} \). Therefore, the correct answer is (2) 1.