A boatman can row a distance of 60 km downstream and return in a total of 15 hours. If the speed of boat downstream is twice its speed upstream, find the time taken by the boat to cover the round trip of 60 km in still water.

Let's break down the problem to find the time taken by the boat to cover the round trip of 60 km in still water.

### Step 1: Define the variables
- Let the speed of the boat in still water be \( x \) km/h.
- Let the speed of the stream be \( y \) km/h.

### Step 2: Speed downstream and upstream
- Speed downstream (with the current) = \( x + y \) km/h.
- Speed upstream (against the current) = \( x - y \) km/h.

### Step 3: Given conditions
- The boatman can row 60 km downstream and return (60 km upstream) in 15 hours.
- The speed downstream is twice the speed upstream. Therefore:
  \[
  x + y = 2(x - y)
  \]

### Step 4: Solve for \( y \)
Expanding the equation:
\[
x + y = 2x - 2y
\]
Bring like terms together:
\[
x - 2x = -2y - y
\]
\[
-x = -3y
\]
\[
y = \frac{x}{3}
\]

So, the speed of the stream \( y = \frac{x}{3} \).

### Step 5: Express time taken downstream and upstream
- Time taken downstream = \( \frac{60}{x + y} \) hours.
- Time taken upstream = \( \frac{60}{x - y} \) hours.

### Step 6: Total time taken for the round trip
The total time is given as 15 hours:
\[
\frac{60}{x + y} + \frac{60}{x - y} = 15
\]

Substituting \( y = \frac{x}{3} \) into the equation:
\[
\frac{60}{x + \frac{x}{3}} + \frac{60}{x - \frac{x}{3}} = 15
\]

### Step 7: Simplify the equation
Simplify the fractions:
\[
\frac{60}{\frac{4x}{3}} + \frac{60}{\frac{2x}{3}} = 15
\]

\[
\frac{60 \times 3}{4x} + \frac{60 \times 3}{2x} = 15
\]

\[
\frac{180}{4x} + \frac{180}{2x} = 15
\]

\[
\frac{45}{x} + \frac{90}{x} = 15
\]

\[
\frac{135}{x} = 15
\]

### Step 8: Solve for \( x \)
\[
x = \frac{135}{15} = 9 \text{ km/h}
\]

### Step 9: Calculate time in still water
The boat's speed in still water is \( x = 9 \) km/h. The time taken to cover the round trip of 60 km in still water (30 km each way) is:

\[
\text{Time in still water} = \frac{60}{9} = \frac{20}{3} \text{ hours} \approx 6.67 \text{ hours}
\]

So, the time taken by the boat to cover the round trip of 60 km in still water is approximately **6.67 hours**.

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Would you like further details on any part of this solution, or do you have any questions?

Here are five related questions you might find interesting:
1. What would be the time taken if the boatman rows the same distance upstream and downstream at equal speeds?
2. How would the problem change if the total distance was 100 km instead of 60 km?
3. How can we determine the speed of the stream directly from the given conditions?
4. What if the downstream speed was three times the upstream speed?
5. How would varying the speed of the stream affect the total time taken for the trip?

**Tip:** When solving problems involving speed and time, setting up clear equations based on given conditions can help simplify the process of finding the solution.

Explore how to calculate the time taken by a boat to cover a round trip of 60 km in still water. This problem involves understanding speed, distance, and time relationships, with detailed steps and solutions provided.

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