A man can row 5 km/h in still water. If the speed of the current is 1 km/h, it takes 3 hrs more in upstream than in the downstream for the same distance. the distance is:

The correct option is 36km.

Step-by-Step Explanation:

1. Identify the given values:
Speed of the man in still water (u) = 5 km/h
Speed of the current (v) = 1 km/h

2. Calculate Upstream and Downstream speeds:
Downstream speed (Speed going with the current) = u + v = 5 + 1 = 6 km/h
Upstream speed (Speed going against the current) = u - v = 5 - 1 = 4 km/h

3. Formulate the equation based on time:
Let the distance be $d$ km.
We know that Time = Distance / Speed.
Time taken downstream ($t_{\text{down}}$) = $\frac{d}{6}$ hours.
Time taken upstream ($t_{\text{up}}$) = $\frac{d}{4}$ hours.

According to the question, upstream time is 3 hours more than downstream time:
$t_{\text{up}}-t_{\text{down}}=3$

$\frac{d}{4}-\frac{d}{6}=3$

4. Solve for $d$:
Taking the LCM of 4 and 6, which is 12:
$\frac{3d-2d}{12}=3$

$\frac{d}{12}=3$

$d=3\times 12=36$ km.

Thus, the distance is 36 km.