A boat takes twice as long to go upstream as to cover the same distance downstream. What is the ratio of the boat's speed in still water to the speed of the stream?

For the same distance, the leg that takes twice as long must be half as fast. So write downstream speed = 2 x upstream speed and solve for b in terms of s. This turns a word puzzle into a one-line equation.

Question: Upstream time = 2 x downstream time for the same distance. Find b : s.

1. Speed is inversely proportional to time, so downstream speed = 2 x upstream speed.
2. b + s = 2(b - s) = 2b - 2s.
3. 3s = b, so b : s = 3 : 1.

Check with numbers: b = 9, s = 3. Downstream 12 km/h, upstream 6 km/h. 24 km takes 2 h down and 4 h up. Twice as long.

General form: if upstream takes n times as long, (b + s) = n(b - s), so b : s = (n + 1) : (n - 1). For n = 3, b : s = 2 : 1.

const ratio = n => (n + 1) / (n - 1);
console.log(ratio(2)); // Output: 3
console.log(ratio(3)); // Output: 2

• Writing b - s = 2(b + s), which puts the factor on the wrong side.
• Giving the ratio of downstream to upstream speeds (2 : 1) instead of boat to stream.