Flynn, Billy and Albert started walking at the same time from the same starting point round a circular track. Albert walked in the clockwise direction. Flynn and Billy walked in an anti-clockwise direction. Albert took 6 min to complete each round. He met Flynn after every 2 minutes. He met Billy after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Albert complete in 1 h?
- When Albert and Flynn met again at the starting point after 1 h, Billy had completed 2.5 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Albert completed in 1 h
= 60 ÷ 6
= 10
(b)
Albert took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Albert's distance is the repeated identity.
Make Albert's distance the same.
Albert's distance : Flynn's distance
2 : 6 - 2
2 : 4
Albert's distance : Billy's distance
5 : 6 - 5
5 : 1
Albert |
Flynn |
Billy |
2x5 |
4x5 |
|
5x2 |
|
1x2 |
10 |
20 |
2 |
The distance of Albert is the repeated identity.
LCM of 2 and 5 = 10
In 1 h
Albert's rounds : Flynn's rounds : Billy's rounds
10 : 20 : 2
Distance that Billy completed in 1 h = 2.5 km
2 rounds = 2.5 km = 2500 m
1 round = 2500 ÷ 2 = 1250 m
Circumference of the circular track = 1250 m
Answer(s): (a) 10; (b) 1250 m