Calculating Total Time for Ship Journey

This problem involves calculating the total time taken for a round trip where the boat travels both downstream and upstream relative to the water current.

Given Information:

• Speed of the ship in still water ($S_s$): 5 km/hr
• Speed of the stream ($S_{st}$): 2 km/hr
• Distance to the place ($d$): 21 km

Calculate Downstream and Upstream Speeds:

When traveling downstream (with the stream), the speeds add up.

Downstream Speed ($S_d$): $S_s + S_{st} = 5 \text{ km/hr} + 2 \text{ km/hr} = 7 \text{ km/hr}$

When traveling upstream (against the stream), the speed of the stream is subtracted from the ship's speed.

Upstream Speed ($S_u$): $S_s - S_{st} = 5 \text{ km/hr} - 2 \text{ km/hr} = 3 \text{ km/hr}$

Calculate Time for Each Leg of the Journey:

Time = Distance / Speed.

Time taken downstream ($t_d$): $\frac{d}{S_d} = \frac{21 \text{ km}}{7 \text{ km/hr}} = 3 \text{ hours}$

Time taken upstream ($t_u$): $\frac{d}{S_u} = \frac{21 \text{ km}}{3 \text{ km/hr}} = 7 \text{ hours}$

Calculate Total Time Taken:

The total time is the sum of the time taken for the downstream and upstream journeys.

Total Time ($T$): $t_d + t_u = 3 \text{ hours} + 7 \text{ hours} = 10 \text{ hours}$

Therefore, the total time taken by Rohan is 10 hours.