Rowing against and with the stream: A man rows 3/4 km upstream in 15 minutes and returns the same 3/4 km downstream in 10 minutes. What is the ratio of his speed in still water to the speed of the current?

Introduction / Context:
Questions on boats and streams use effective speeds: upstream speed = (boat speed in still water - current speed) and downstream speed = (boat speed in still water + current speed). By comparing times for the same distance, we can solve for the ratio of speeds.

Given Data / Assumptions:

• Upstream distance = 0.75 km covered in 15 minutes = 0.25 h.
• Downstream distance = 0.75 km covered in 10 minutes = 1/6 h.
• Let boat speed in still water = b km/h, current speed = c km/h.

Concept / Approach:
Upstream speed is b - c. Downstream speed is b + c. For a fixed distance, speed = distance / time. We compute the two effective speeds from the observed times, then solve for b and c and report the ratio b : c.

Step-by-Step Solution:
Upstream speed = 0.75 / 0.25 = 3 km/h Downstream speed = 0.75 / (1/6) = 4.5 km/h So b - c = 3 and b + c = 4.5 Add: 2b = 7.5 ⇒ b = 3.75 km/h Subtract: 2c = 1.5 ⇒ c = 0.75 km/h Ratio b : c = 3.75 : 0.75 = 5 : 1

Verification / Alternative check:
Plug back: upstream = 3.75 - 0.75 = 3 km/h; downstream = 3.75 + 0.75 = 4.5 km/h — matches computed values; times are consistent.

Why Other Options Are Wrong:
3 : 5 or 1 : 5 would imply the current is faster than the boat, which contradicts the data. 5 : 3 does not satisfy the two equations simultaneously. 'None of these' is invalid because 5 : 1 fits perfectly.

Common Pitfalls:
Using minutes directly without converting to hours; inverting ratios; assuming the ratio of times equals the ratio of speeds rather than the inverse for the same distance.

Final Answer:
5 : 1