Question

A man can row a boat in still water at the rate of 17 km/hr. He finds that it takes him thrice as long to row upstream of a river as to row downstream of the same river. The speed of of the stream is,

• A. 15 km/hr
• B. 11.5 km/hr
• C. 8.5 km/hr
• D. 6 km/hr

Hint:

Upstream speed is one third of downstream speed. Solve \(17 - s = \frac{17+s}{3}\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When a boat goes downstream, the stream helps it, so the speed is boat speed plus stream speed. When it goes upstream, the stream opposes it, so the speed is boat speed minus stream speed.

Step 2: Set up the symbols.
Let the stream speed be \(s\) km/hr. The boat speed in still water is 17 km/hr.
Downstream speed \(= 17 + s\).
Upstream speed \(= 17 - s\).

Step 3: Use the time condition.
For the same distance, time is inversely proportional to speed. Upstream time is 3 times the downstream time, so the upstream speed is one third of the downstream speed.
\[ 17 - s = \frac{17 + s}{3} \]
Multiply both sides by 3:
\[ 51 - 3s = 17 + s \]
\[ 34 = 4s \]
\[ s = 8.5 \]

Step 4: Check the options.
With \(s = 8.5\), downstream speed is 25.5 km/hr and upstream speed is 8.5 km/hr. The ratio is 3 : 1, which matches the condition.
If \(s = 15\), the upstream speed is only 2 km/hr and the ratio is 16, so option 1 is wrong.
If \(s = 11.5\), the speeds are 28.5 and 5.5, ratio about 5.2, so option 2 is wrong.
If \(s = 6\), the speeds are 23 and 11, ratio about 2.1, so option 4 is wrong.

Final Answer:
The speed of the stream is 8.5 km/hr, which is option 3. \[ \boxed{8.5 \text{ km/hr}} \]