Understanding the Problem

We are given the rowing speeds of Sindbad in two different scenarios:
1. He rows 24 km upstream and 54 km downstream in 6 hours.
2. He rows 36 km upstream and 48 km downstream in 8 hours.

We need to find Sindbad’s speed in still water.

Let’s denote:
– Sindbad’s speed upstream as \(x\) km/h.
– Sindbad’s speed downstream as \(y\) km/h.

Solving the Problem

From the given scenarios, we can write two equations:

1. For the first scenario:

\[ \frac{24}{x} + \frac{54}{y} = 6 \]

Simplifying, we get:

\[ \frac{4}{x} + \frac{9}{y} = 1 \text{ —- Eqn(1)} \]

2. For the second scenario:

\[ \frac{36}{x} + \frac{48}{y} = 8 \]

Simplifying, we get:

\[ \frac{9}{x} + \frac{12}{y} = 2 \text{ —- Eqn(2)} \]

Solving equations (1) and (2), we find:

\[ x = \frac{11}{2} \text{ km/h} \text{ (Sindbad’s speed upstream)} \]
\[ y = 33 \text{ km/h} \text{ (Sindbad’s speed downstream)} \]

Sindbad’s speed in still water is the average of his speeds upstream and downstream:

\[ \text{Speed in still water} = \frac{x + y}{2} = \frac{\frac{11}{2} + 33}{2} = \frac{77}{4} = 19.25 \text{ km/h} \]

Conclusion

Sindbad’s speed in still water is 19.25 km/h.

Let’s solve this step by step.

First, let’s find out how much work Vasant can complete in one day. Since Vasant can do the entire piece of work in 24 days, his work rate is:

\[
\text{Vasant’s work rate} = \frac{1}{24} \text{ (work per day)}
\]

Vasant works alone for 4 days, so the fraction of the work he completes is:

\[
\text{Work done by Vasant} = 4 \times \frac{1}{24} = \frac{1}{6}
\]

This means that after Vasant works for 4 days, \(\frac{1}{6}\) of the work is done and \(\frac{5}{6}\) of the work is remaining.

Ritu completes the remaining \(\frac{5}{6}\) of the work in 25 days. So, Ritu’s work rate is:

\[
\text{Ritu’s work rate} = \frac{\frac{5}{6}}{25} = \frac{1}{30} \text{ (work per day)}
\]

Now, we want to find out how long it would take for Vasant and Ritu to complete the work together. The combined work rate of Vasant and Ritu is:

\[
\text{Combined work rate} = \text{Vasant’s work rate} + \text{Ritu’s work rate} = \frac{1}{24} + \frac{1}{30}
\]

To find the time taken for them to complete the work together, we take the reciprocal of their combined work rate:

\[
\text{Time taken together} = \frac{1}{\text{Combined work rate}} = \frac{1}{\frac{1}{24} + \frac{1}{30}}
\]

Let’s calculate the exact value of the time taken together using this formula.

The time taken for Vasant and Ritu to complete the work together is:

\[
\text{Time taken together} = \frac{1}{\frac{1}{24} + \frac{1}{30}} = \frac{1}{\frac{30 + 24}{24 \times 30}} = \frac{24 \times 30}{54} = \frac{720}{54} = \frac{40}{3} = 13\frac{1}{3} \text{ days}
\]

So, Vasant and Ritu together can complete the work in \(13\frac{1}{3}\) days.