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

Check option 2 directly: boat speed $b = 9$ km/h, stream speed $s = 3$ km/h.
Original downstream speed is $9+3=12$ km/h and upstream speed is $9-3=6$ km/h. Time for $28$ km upstream is $28/6$ hours and downstream is $28/12$ hours, and $28/6$ is exactly twice $28/12$, so the first condition holds.
Now double the stream speed to $6$ km/h. New downstream speed is $9+6=15$ km/h and new upstream speed is $9-6=3$ km/h.
Total time $= \dfrac{28}{15} + \dfrac{28}{3}$ hours $= 1.867 + 9.333 = 11.2$ hours $= 672$ minutes, matching the given condition exactly.
\[\boxed{9 \text{ km/hr boat speed, } 3 \text{ km/hr stream speed}}\]