A hard question on meeting for P5, with a step-by-step solution, diagrams and the answer. The basis of journey problems: meeting and catching up appear in the Hua Xia Cup's P4 to P6 qualifying rounds and finals.
The question
Two brothers live at the two ends of a straight road, 780 m apart.
The younger sets off first, walking towards his brother's home.
6 minutes later the older one sets off towards him with his dog.
The older walks 50 m a minute, the younger 40 m a minute.
The dog runs 120 m a minute: it runs to the younger brother, turns straight back to the older one, turns again, and keeps running to and fro until the brothers meet.
How far does the dog run altogether?
Show the hints (3)
💡Hint 1: Don't add up the dog's trips one by one. For how many minutes does the dog run?
💡Hint 2: When the older brother and the dog set off, how far apart are the brothers?
💡Hint 3: They are then 540 m apart and close 90 m a minute; the dog runs from that moment until they meet.
Worked solution
Have a go first, then read the solution step by step.
1.The younger walks 40 × 6 = 240 m first, leaving 780 − 240 = 540 m between them.
2.Then they close 50 + 40 = 90 m a minute: 540 ÷ 90 = 6 minutes until they meet.
3.The dog runs to and fro until the brothers meet: 6 minutes in all, so 120 × 6 = 720 m.
⚠️Common mistake: counting the younger brother's 6-minute head start as running time for the dog. The dog sets off with the older brother.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download