A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

To solve this problem, we need to understand that the speed of the boat in still water and the speed of the current affect the boat's speed when it's going upstream and downstream.

Let's denote:

• the speed of the boat in still water as 'b' (in km/h),
• the speed of the current as 'c' (in km/h).

When the boat is going downstream (with the current), its effective speed is (b+c) km/h. When it's going upstream (against the current), its effective speed is (b-c) km/h.

We know that the boat covers the same distance 'd' (in km) going upstream and downstream. The time it takes to cover this distance is the distance divided by the speed. So we have the following two equations:

1. d / (b - c) = 8 hours 48 minutes = 8.8 hours,
2. d / (b + c) = 4 hours.

We can express 'd' from the first equation: d = 8.8 * (b - c) and substitute it into the second equation:

8.8 * (b - c) / (b + c) = 4.

Solving this equation for b/c gives us the ratio between the speed of the boat and the speed of the water current:

b/c = (4 + 8.8) / (8.8 - 4) = 12.8 / 4.8 = 2.67.

So, the ratio between the speed of the boat and the speed of the water current is 2.67:1.

To find the ratio between the speed of the boat and the speed of the water current, we can use the concept of relative speed.

Let's assume the speed of the boat is B km/h and the speed of the water current is C km/h.

When the boat is running upstream, it is moving against the current. So, the effective speed of the boat is reduced by the speed of the current. Therefore, the speed of the boat relative to the water is (B - C) km/h.

Similarly, when the boat is running downstream, it is moving with the current. So, the effective speed of the boat is increased by the speed of the current. Therefore, the speed of the boat relative to the water is (B + C) km/h.

We are given that the boat takes 8 hours 48 minutes (or 8.8 hours) to cover the distance upstream and 4 hours to cover the same distance downstream.

Using the formula Distance = Speed × Time, we can set up the following equations:

Distance = (B - C) × 8.8 (1) Distance = (B + C) × 4 (2)

Since the distance covered is the same in both cases, we can equate the two equations:

(B - C) × 8.8 = (B + C) × 4

Simplifying this equation, we get:

8.8B - 8.8C = 4B + 4C 4.8B = 13.2C B/C = 13.2/4.8

Therefore, the ratio between the speed of the boat and the speed of the water current is 13.2/4.8, which simplifies to 11/4.