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?

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**Solution:**

1. Let the speed of the boat in still water be *x* and the speed of the current be *y*.

2. Time taken upstream = 8 hours 48 minutes = 8 + \frac{48}{60} = 8.8 hours

3. Time taken downstream = 4 hours

4. Let the distance be *D*.

5. Upstream speed = (x - y), downstream speed = (x + y)

6. Using the formula distance = speed × time, we have:
   - Upstream distance: $D = (x - y) \times 8.8$
   - Downstream distance: $D = (x + y) \times 4$

7. Since the distances are the same:
   $$(x - y) \times 8.8 = (x + y) \times 4$$

8. Expand and rearrange:
   $$8.8x - 8.8y = 4x + 4y$$

9. Bring like terms together:
   $$8.8x - 4x = 8.8y + 4y$$
   $$4.8x = 12.8y$$

10. Divide both sides by y:
    $$\frac{x}{y} = \frac{12.8}{4.8} = \frac{128}{48} = \frac{8}{3}$$

**Answer:** The ratio of the speed of the boat to the speed of the current is $8 : 3$.

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