A boat takes 8 hours 48 minutes to travel a certain distance upstream and 4 hours to cover the same distance downstream. What is the ratio of the speed of the boat in still water to the speed of the water current?

Introduction / Context:
This question deals with the relationship between upstream time, downstream time, and the speeds of a boat and the current. We are not asked for the numerical values of the speeds, but rather for the ratio of the speed of the boat in still water to the speed of the stream. This is a common pattern in aptitude tests and is easy to handle using the standard boats and streams formulas and time relations.

Given Data / Assumptions:

• Upstream time to cover a certain distance = 8 hours 48 minutes.
• Downstream time to cover the same distance = 4 hours.
• Distance is the same in both directions.
• Boat and stream speeds are constant for the entire travel.
• We need the ratio boat speed : current speed.

Concept / Approach:
Let the distance be D, boat speed in still water be b, and current speed be c. Then:

• Upstream speed = b - c = D / T_up.
• Downstream speed = b + c = D / T_down.

Although we do not know D, by expressing b and c in terms of D and times, we can eliminate D and find a ratio b : c using a time based shortcut. The ratio b : c can be written as (T_up + T_down) : (T_up - T_down).

Step-by-Step Solution:
Convert 8 hours 48 minutes into hours: 48 minutes = 48 / 60 = 0.8 hours. So T_up = 8.8 hours and T_down = 4 hours. Let D be the distance. Then upstream speed = D / 8.8 and downstream speed = D / 4. Boat speed b = (upstream speed + downstream speed) / 2. Stream speed c = (downstream speed - upstream speed) / 2. Thus b : c = (T_up + T_down) : (T_up - T_down). Compute T_up + T_down = 8.8 + 4 = 12.8. Compute T_up - T_down = 8.8 - 4 = 4.8. So b : c = 12.8 : 4.8. Divide both terms by 0.8 to simplify: 12.8 / 0.8 = 16 and 4.8 / 0.8 = 6, so ratio = 16 : 6. Further simplify by dividing by 2 to get 8 : 3.

Verification / Alternative check:
If we assume D = 1 unit for convenience, upstream speed is 1 / 8.8 and downstream speed is 1 / 4. Then b = (1 / 8.8 + 1 / 4) / 2 and c = (1 / 4 - 1 / 8.8) / 2. Computing these values and then forming b : c yields the same ratio 8 : 3 after simplification. Therefore the shortcut using times is reliable and confirms the result.

Why Other Options Are Wrong:
Ratios such as 7:4, 11:4, and 4:7 do not correspond to the time combination pattern. If we tried to reconstruct speeds using these ratios, the implied upstream and downstream times would not match 8 hours 48 minutes and 4 hours. Only 8:3 is consistent with the given timings.

Common Pitfalls:
A typical mistake is to attempt to find absolute speeds with an assumed distance but then lose track of simplifying to a ratio. Another error is to forget converting 48 minutes into hours, which changes the value of T_up. Some learners also guess that the ratio must be T_up : T_down, which is not correct. Remember that the correct time based ratio for b : c is (T_up + T_down) : (T_up - T_down).

Final Answer:
The required ratio of the speed of the boat in still water to the speed of the current is 8:3.