A boat running downstream takes 3 hours to cover a certain distance, while it takes 6 hours 40 minutes to cover the same distance running upstream. What is the ratio between the speed of the boat and speed of the water current respectively?

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 downstream, it gets the additional speed of the water current, so its effective speed becomes (B + C) km/h. We are given that it takes 3 hours to cover the distance in this case.

Similarly, when the boat is running upstream, it goes against the water current, so its effective speed becomes (B - C) km/h. We are given that it takes 6 hours 40 minutes (or 6.67 hours) to cover the distance in this case.

Now, we can use the formula: Distance = Speed × Time.

For the downstream journey, the distance covered is the same as the distance covered in the upstream journey. Let's call this distance D.

So, for the downstream journey, we have D = (B + C) × 3.

And for the upstream journey, we have D = (B - C) × 6.67.

Since both equations represent the same distance, we can equate them:

(B + C) × 3 = (B - C) × 6.67.

Now, we can solve this equation to find the ratio between B and C.

Expanding the equation, we get:

3B + 3C = 6.67B - 6.67C.

Bringing like terms together, we have:

6.67B - 3B = 6.67C + 3C.

Simplifying further, we get:

3.67B = 9.67C.

Dividing both sides by 9.67C, we get:

B/C = 9.67/3.67.

Therefore, the ratio between the speed of the boat and the speed of the water current is approximately 2.64.