If a boy walks to school at 5 km/h he is 7 minutes late; at 6 km/h he is 5 minutes early. How far is the school?
6 km. The two journey times differ by 7 + 5 = 12 minutes = 1/5 hour. So d/5 - d/6 = 1/5, which gives d/30 = 1/5 and d = 6 km.
Explain it simply
Being late in one case and early in the other means the two travel times differ by the sum of the two amounts. If both cases were late (or both early), the difference would be the gap between them. Once you know the time difference, one equation in the distance does the job.
Example
Question: At 5 km/h he is 7 min late; at 6 km/h, 5 min early. Distance?
- Time difference = 7 + 5 = 12 minutes = 12/60 = 1/5 hour.
- d/5 - d/6 = 1/5.
- d (6 - 5) / 30 = 1/5, so d/30 = 1/5 and d = 6 km.
Check: at 5 km/h he takes 72 min; at 6 km/h, 60 min. So the right time must be 65 minutes: 72 is 7 late and 60 is 5 early. Correct.
Shortcut: d = (product of speeds / difference of speeds) x time difference = (30 / 1) x 1/5 = 6 km.
const d = ((5 * 6) / (6 - 5)) * (12 / 60);
console.log(Math.round(d * 100) / 100); // Output: 6What to say in the interview
"Late by 7 and early by 5 means the two times differ by 12 minutes, a fifth of an hour. d over 5 minus d over 6 equals a fifth, so d is 6 km. The times 72 and 60 minutes around a 65-minute target confirm it."
Common mistakes
- Using 7 - 5 = 2 minutes as the difference.
- Leaving the time in minutes while speeds are in km/h.