Explanation:

Let’s break this down step by step:

- Let the speed of the boat in still water be \( x \). The speed of the current is \( y \).

- Downstream speed = \( x + y \)

- Upstream speed = \( x - y \)

Here’s what you know:

1. Time = Distance / Speed

First scenario: \( \frac{40}{x+y} + \frac{25}{x-y} = 7.5 \)

2. Second scenario: \( \frac{48}{x+y} + \frac{36}{x-y} = 10 \)

Now, let’s solve these.

Let’s call \( A = \frac{1}{x+y} \), \( B = \frac{1}{x-y} \).

- 40A + 25B = 7.5 ... (1)

- 48A + 36B = 10 ... (2)

Multiply (1) by 36 and (2) by 25 to eliminate B:

- 40A*36 + 25B*36 = 7.5*36 ? 1440A + 900B = 270

- 48A*25 + 36B*25 = 10*25 ? 1200A + 900B = 250

Subtract these:

(1440A + 900B) - (1200A + 900B) = 270 - 250

So: 240A = 20 ? A = 1/12

That means \( x+y = 12 \).

Plug A back into (1):

40*(1/12) + 25B = 7.5

(10/3) + 25B = 7.5

25B = 7.5 - 10/3 = 7.5 - 3.33 = 4.17

B = 4.17 / 25 ˜ 0.167 ? B ˜ 1/6

So \( x - y = 6 \).

Now add \( x+y = 12 \) and \( x-y = 6 \):

2x = 18 ? x = 9

So, the correct answer is:

Option 3: 9 km/h

Here’s what the other options would mean:

- 1 km/h or 6 km/h — the boat would be slower than a cyclist or about jogging speed. Doesn’t fit.

- 12 km/h — sounds logical but, after calculation, not correct.

- 15 km/h — a bit fast for this data.

So, your instinct was spot-on. The speed of the boat in still water is 9 km/h.