# Number Problem 21

### From Homeworkwiki

**From A, a young man takes 20 minutes to reach his work spot whereas an old man takes 30 minutes.**

**When will the young man catch up the old man if the latter starts 5 minutes before him?**

**Solution:** The speed of the young man : The speed of the old man = 1/20 : 1/30 = 3 : 2

Let the speed of the young man be 3x meters per minute and that of the old man be 2x meters per minute.

If the young man takes y minutes to catch up the old man, then the distance traversed by him = 3xy meters.

The distance traversed by the old man = 2x (y + 5) meters

3xy = 2x (y + 5)

3y = 2(y + 5)

y = 10

The young man will catch the old man 10 minutes after his start.