A boat takes a total of 4 hours to travel 14 km upstream and 36 km downstream. It takes 5 hours to travel 20 km upstream and 24 km downstream. Let the speed of the boat in still water be $x$ km/h and the speed of the current be $y$ km/h.

Using the given information, find the speed of the boat in still water.

Question

A boat takes a total of 4 hours to travel 14 km upstream and 36 km downstream. It takes 5 hours to travel 20 km upstream and 24 km downstream. Let the speed of the boat in still water be $x$ km/h and the speed of the current be $y$ km/h.

Using the given information, find the speed of the boat in still water.

Accepted Answer

**Solution:**

1. Let the speed of the boat in still water be $x$ km/h and the speed of the current be $y$ km/h.

2. From the problem, we have two equations based on time taken:

- For 14 km upstream and 36 km downstream in 4 hours:
     $$\frac{14}{x - y} + \frac{36}{x + y} = 4 \quad ...(i)$$

- For 20 km upstream and 24 km downstream in 5 hours:
     $$\frac{20}{x - y} + \frac{24}{x + y} = 5 \quad ...(ii)$$

3. Multiply equation (ii) by 7/4 and subtract equation (i) multiplied by 5/4 to eliminate one variable or use a suitable combination. Alternatively, multiply equation (ii) by 3 and equation (i) by 4 and subtract:

$$3 	imes (ii): \frac{60}{x - y} + \frac{72}{x + y} = 15$$

$$4 	imes (i): \frac{56}{x - y} + \frac{144}{x + y} = 16$$

Subtracting:

$$\left(\frac{60}{x - y} - \frac{56}{x - y}ight) + \left(\frac{72}{x + y} - \frac{144}{x + y}ight) = 15 - 16$$

$$\frac{4}{x - y} - \frac{72}{x + y} = -1$$

This can be rearranged to find $x - y$ and $x + y$.

4. From the given solution steps, it is found that:

$$x - y = \frac{32}{7} \approx 4.57 	ext{ km/h}$$

$$x + y = \frac{192}{5} = 38.4 	ext{ km/h}$$

5. Adding these two equations:

$$2x = \frac{32}{7} + \frac{192}{5} = \frac{160}{35} + \frac{1344}{35} = \frac{1504}{35}$$

$$x = \frac{1504}{70} = \frac{752}{35} \approx 21.48 	ext{ km/h}$$

**Answer:** The speed of the boat in still water is approximately $21.48 	ext{ km/h}$.

Answer

Answer

Answer