Question

A man went downstream for 28 km in a motor boat and immediately returned. It took the man twice as long to make the return trip. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. Find the speed of the boat in still water and the speed of the river flow.

• A. 12 km/hr, 3 km/hr
• B. 9 km/hr, 3 km/hr
• C. 8 km/hr, 2 km/hr
• D. 9 km/hr, 6 km/hr

Hint:

First use the time relation to link boat and stream speed, then apply the doubled stream speed condition.

Answer 1

The Correct Option is B

Step 1: Let boat speed in still water be \(b\) km/h and stream speed be \(s\) km/h.
Step 2: Downstream speed = \(b+s\), upstream speed = \(b-s\). Time upstream is twice time downstream, so \(\dfrac{28}{b-s} = 2 \times \dfrac{28}{b+s}\), giving \(b+s = 2(b-s)\), so \(b = 3s\).
Step 3: If stream speed doubles to \(2s\), new downstream speed = \(b+2s = 5s\) and new upstream speed = \(b-2s = s\).
Step 4: Total time = \(\dfrac{28}{5s} + \dfrac{28}{s} = 11.2\) hours (672 minutes).
Step 5: Solving this equation gives \(s = 3\) km/h and \(b = 3s = 9\) km/h.