Question

A boat goes 16 km upstream and 24 km downstream in 6 hours. It can go 12 km upstream and 36 km downstream in the same time. The speed of the boat in still water is:

• A. 8 km/hr
• B. 7 km/hr
• C. 6 km/hr
• D. 7.6 km/hr

Hint:

When solving boat-related problems, set up equations based on the speed of the boat upstream and downstream, then solve the system of equations.

Answer 1

The Correct Option is A

Let the speed of the boat in still water be \( b \) km/hr, and the speed of the current be \( c \) km/hr. 
Step 1: The effective speed upstream is \( b - c \) and downstream is \( b + c \). Using the time taken for each journey, we have the following equations: \[ \frac{16}{b - c} + \frac{24}{b + c} = 6 \quad \text{(Equation 1)} \] \[ \frac{12}{b - c} + \frac{36}{b + c} = 6 \quad \text{(Equation 2)} \] 
Step 2: Solve these two equations simultaneously. After solving the system of equations, we find: \[ b = 8 \, \text{km/hr} \] Thus, the speed of the boat in still water is 8 km/hr.