Question

A boat can go \( 1 \frac{3}{5} \) km upstream and \( 4 \frac{4}{5} \) km downstream in 48 minutes, while it can go 2 km upstream and 600 m downstream in 33 minutes. How much time (in hours) will it take to go 28.8 km downstream?

• A. 1.8
• B. 1.92
• C. 2.4
• D. 3.2

Hint:

In problems involving upstream and downstream motion, first calculate the boat’s effective speed for both directions and use it to calculate the time for longer distances.

Answer 1

The Correct Option is C

Let the speed of the boat in still water be \( v_b \) km/h and the speed of the stream be \( v_s \) km/h.
The boat's effective speed downstream is \( v_b + v_s \) and upstream is \( v_b - v_s \).
Using the data provided, set up equations based on the time taken and solve for the effective speed downstream.
Finally, calculate the time to cover 28.8 km downstream using the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \).