Ishwar rows a boat. He takes half as much time to go a certain distance downstream as he takes to cover the same distance upstream. What is the ratio of the rate of the boat in still water to the rate of the current?

Introduction / Context:
Time ratios for equal distances translate into relationships between effective speeds. If one leg takes half the time of the other, then the corresponding speed must be double. This fact helps connect the boat speed in still water and the current speed using v ± c.

Given Data / Assumptions:

• D/(v + c) = (1/2) * D/(v − c).
• v is still water speed; c is current speed.
• Same distance both ways; constant speeds.

Concept / Approach:
Cancel D to obtain 1/(v + c) = (1/2)/(v − c). Cross-multiply to form a linear relation and solve for v in terms of c; then express v : c.

Step-by-Step Solution:

Verification / Alternative check:
Assume v = 3 and c = 1 (arbitrary units). Then downstream speed = 4, upstream speed = 2. Times are D/4 and D/2—indeed, downstream time is half of upstream time.

Why Other Options Are Wrong:
2:1, 5:1, 7:1 do not maintain the required halving of time for equal distances.

Common Pitfalls:
Reversing the ratio or confusing whether time or speed is halved or doubled. Remember time and speed are inversely related for a fixed distance.

Final Answer:
3 : 1