A boat covers a distance of $180 ext{ km}$ downstream and $150 ext{ km}$ upstream in a total of $5$ hours. The ratio of the speed of the boat in still water to the speed of the stream is $7:2$. What is the time taken by the boat to travel $315 ext{ km}$ in still water?

Question

A boat covers a distance of $180 		ext{ km}$ downstream and $150 		ext{ km}$ upstream in a total of $5$ hours. The ratio of the speed of the boat in still water to the speed of the stream is $7:2$. What is the time taken by the boat to travel $315 		ext{ km}$ in still water?

Accepted Answer

**Solution:**

1. Let the speed of the boat in still water be $7x$ km/h and the speed of the stream be $2x$ km/h.

2. Then, the downstream speed = speed of boat + speed of stream = $7x + 2x = 9x$ km/h.

3. The upstream speed = speed of boat - speed of stream = $7x - 2x = 5x$ km/h.

4. Given that the boat covers $180$ km downstream and $150$ km upstream in $5$ hours:
   
   $$\frac{180}{9x} + \frac{150}{5x} = 5$$

5. Simplify the equation:
   
   $$\frac{180}{9x} = \frac{20}{x}, \quad \frac{150}{5x} = \frac{30}{x}$$

So,

$$\frac{20}{x} + \frac{30}{x} = 5 \implies \frac{50}{x} = 5$$

6. Solving for $x$:

$$x = \frac{50}{5} = 10$$

7. Therefore, speed of boat in still water = $7x = 7 	imes 10 = 70$ km/h.

8. Time taken to cover $315$ km in still water:

$$	ext{Time} = \frac{	ext{Distance}}{	ext{Speed}} = \frac{315}{70} = 4.5 	ext{ hours}$$

**Answer:** $4.5 	ext{ hours}$

Answer

Answer

Answer

Answer