Sindbad rows 24 km against the flow of water and 54 km with the flow of water in 6 hours. He can also row 36 km against the flow and 48 km with the flow in 8 hours. What is his speed in still water?

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.