A boat can row 20 km downstream and 20 km upstream in 12 hours. If the speed of the boat in still water is 50\% more than the speed of the stream, find the time taken by the boat to cover 50 km downstream.

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**Solution:**

1. Let the speed of the stream be *x* km/h. Then, the speed of the boat in still water is *1.5x* km/h (50\% more than the stream speed).

2. Speed downstream = speed of boat + speed of stream = $1.5x + x = 2.5x$ km/h.

3. Speed upstream = speed of boat - speed of stream = $1.5x - x = 0.5x$ km/h.

4. Given that the boat covers 20 km downstream and 20 km upstream in 12 hours:
   
   $$\frac{20}{2.5x} + \frac{20}{0.5x} = 12$$

5. Simplify the equation:
   
   $$\frac{20}{2.5x} = \frac{20}{\frac{5}{2}x} = \frac{20 	imes 2}{5x} = \frac{40}{5x} = \frac{8}{x}$$

$$\frac{20}{0.5x} = \frac{20}{\frac{1}{2}x} = \frac{20 	imes 2}{x} = \frac{40}{x}$$

6. Substitute back:
   
   $$\frac{8}{x} + \frac{40}{x} = 12$$

$$\frac{48}{x} = 12$$

7. Solve for *x*:
   
   $$x = \frac{48}{12} = 4 	ext{ km/h}$$

8. Speed downstream = $2.5x = 2.5 	imes 4 = 10$ km/h.

9. Time to cover 50 km downstream:
   
   $$	ext{Time} = \frac{	ext{Distance}}{	ext{Speed}} = \frac{50}{10} = 5 	ext{ hours}$$

**Answer:** 5 hours

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