Walking at 3/4 of his usual speed, a student reaches college 20 minutes late. What is his usual time for the journey?
60 minutes. For a fixed distance, time is inversely proportional to speed. At 3/4 speed the time becomes 4/3 of usual, so the extra 1/3 of the usual time equals 20 minutes and the usual time is 60 minutes.
Explain it simply
On the same route, if you go slower, you take proportionally longer. Speed and time move in opposite ratios: speed 4 : 3 means time 3 : 4. The difference of one part in time is the 20 minutes he is late by, so you can read off the usual time directly.
Example
Question: At 3/4 of usual speed he is 20 minutes late. Find the usual time.
- Speed ratio usual : new = 4 : 3.
- Time ratio usual : new = 3 : 4.
- Difference = 1 part = 20 minutes.
- Usual time = 3 parts = 60 minutes.
Check: if usual time is 60 min, new time = 60 x 4/3 = 80 min, which is 20 min late.
Related form: at 5/6 of usual speed a train is 10 minutes late. Time ratio 5 : 6, one part = 10 minutes, usual time = 50 minutes.
const usual = 20 / (4 / 3 - 1);
console.log(Math.round(usual)); // Output: 60What to say in the interview
"Same distance, so time is inversely proportional to speed. Three quarters the speed means four thirds the time. The extra third is 20 minutes, so the usual time is an hour."
Common mistakes
- Calculating 3/4 of the time instead of 4/3.
- Giving the new time (80 minutes) when asked for the usual time.