Question : A boat takes 11 hours to travel a distance upstream and takes 5 hours to travel the same distance downstream. If the speed of the boat in still water is $2 \frac{2}{9}$ m/s, then the speed of the stream (in km/hr) is:
Option 1: 2
Option 2: 3
Option 3: 1
Option 4: 4
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Correct Answer: 3
Solution :
Let us assume $B$ as the speed of the boat in still water (m/s) and $S$ as the speed of the stream (m/s)
Effective speed upstream = (B – S) m/s
Effective speed downstream = (B + S) m/s
For upstream:
Distance = (B – S) $\times$ 11 hours
For downstream:
Distance = (B + S) $\times$ 5 hours
Since distance is the same in both cases, we can equate the right sides of the two equations:
$\therefore$ 11 (B – S) = 5 (B + S)
On solving, we get,
⇒ B = $\frac{8}{3}$S
The speed of the boat in still water is $2 \frac{2}{9}$ m/s, which can be converted to km/hr:
$2 \frac{2}{9}$ m/s = $\left(\frac{20}{9}\right) \times \frac{18}{5}$ km/hr = $8$ km/hr
Now, we can find the speed of the stream (S):
B = $8$ km/hr = $\left(\frac{8}{3}\right)S$
S = $\frac{3}{8} \times 8$ km/hr = 3 km/hr
Hence, the correct answer is 3.
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