A boat covers a fixed distance upstream in 528 minutes and the same distance downstream in 240 minutes. Find the ratio of the boat's speed in still water to the speed of the current.

Introduction / Context:
This problem compares times to travel the same distance upstream and downstream to extract the speeds in still water and current via ratios.

Given Data / Assumptions:

• Upstream time Tu = 528 minutes = 8.8 h.
• Downstream time Td = 240 minutes = 4 h.
• Let boat speed in still water = b, current speed = c (km/h), distance = D km.

Concept / Approach:
Upstream speed = b - c; downstream speed = b + c. Since D is the same, ratios of speeds equal inverse ratios of times: (b - c)/(b + c) = Td/Tu.

Step-by-Step Solution:
(b - c)/(b + c) = 4 / 8.8 = 5 / 11 11(b - c) = 5(b + c) 11b - 11c = 5b + 5c ⇒ 6b = 16c ⇒ b/c = 16/6 = 8/3

Verification / Alternative check:
Any numbers with b : c = 8 : 3 (for example b = 8, c = 3) satisfy (b - c)/(b + c) = 5/11, which matches 4/8.8.

Why Other Options Are Wrong:
2 : 1 and 3 : 2 do not produce 5/11 on substitution. 'Couldn't be determined' is wrong because the two times are sufficient to determine the ratio uniquely.

Common Pitfalls:
Using Tu/Td instead of Td/Tu; forgetting to convert minutes to hours; cancelling the distance incorrectly.

Final Answer:
8 : 3