A swimmer covers 36 km downstream in 3 hours and 24 km upstream in 4 hours. Find the swimmer's speed in still water and the speed of the current.
SHORT ANSWER
Swimmer 9 km/h and current 3 km/h. Downstream speed = 36/3 = 12 km/h, upstream = 24/4 = 6 km/h. Swimmer = (12 + 6)/2 = 9; current = (12 - 6)/2 = 3.
Explain it simply
First turn the distances and times into the two speeds. After that it is the same pair of equations as every boats question: downstream is the sum, upstream is the difference. Most mistakes happen when people try to average distances or times instead of speeds.
Example
Question: 36 km downstream in 3 h, 24 km upstream in 4 h.
- Downstream speed = 36 / 3 = 12 km/h.
- Upstream speed = 24 / 4 = 6 km/h.
- Swimmer = (12 + 6) / 2 = 9 km/h.
- Current = (12 - 6) / 2 = 3 km/h.
Follow-up: in still water, how long for 27 km? 27 / 9 = 3 hours.
js
const down = 36 / 3, up = 24 / 4;
console.log([(down + up) / 2, (down - up) / 2]); // Output: [9,3]What to say in the interview
"I get the two speeds first: 12 downstream and 6 upstream. Then half the sum is the swimmer's speed, 9, and half the difference is the current, 3."
Common mistakes
- Dividing total distance by total time (60/7) and calling it the still-water speed.
- Mixing up which leg is downstream.