George, Bobby and Henry started walking at the same time from the same starting point round a circular track. Henry walked in the clockwise direction. George and Bobby walked in an anti-clockwise direction. Henry took 6 min to complete each round. He met George after every 2 minutes. He met Bobby after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Henry complete in 1 h?
- When Henry and George met again at the starting point after 1 h, Bobby had completed 2.2 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Henry completed in 1 h
= 60 ÷ 6
= 10
(b)
Henry took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Henry's distance is the repeated identity.
Make Henry's distance the same.
Henry's distance : George's distance
2 : 6 - 2
2 : 4
Henry's distance : Bobby's distance
4 : 6 - 4
4 : 2
Henry |
George |
Bobby |
2x2 |
4x2 |
|
4x1 |
|
2x1 |
4 |
8 |
2 |
The distance of Henry is the repeated identity.
LCM of 2 and 4 = 4
In 1 h
Henry's rounds : George's rounds : Bobby's rounds
4 : 8 : 2
Distance that Bobby completed in 1 h = 2.2 km
2 rounds = 2.2 km = 2200 m
1 round = 2200 ÷ 2 = 1100 m
Circumference of the circular track = 1100 m
Answer(s): (a) 10; (b) 1100 m