Liam, Jack and Fred started walking at the same time from the same starting point round a circular track. Fred walked in the clockwise direction. Liam and Jack walked in an anti-clockwise direction. Fred took 12 min to complete each round. He met Liam after every 2 minutes. He met Jack after every 7 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Fred complete in 1 h?
- When Fred and Liam met again at the starting point after 1 h, Jack had completed 2.4 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Fred completed in 1 h
= 60 ÷ 12
= 5
(b)
Fred took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Fred's distance is the repeated identity.
Make Fred's distance the same.
Fred's distance : Liam's distance
2 : 12 - 2
2 : 10
Fred's distance : Jack's distance
7 : 12 - 7
7 : 5
Fred |
Liam |
Jack |
2x7 |
10x7 |
|
7x2 |
|
5x2 |
14 |
70 |
10 |
The distance of Fred is the repeated identity.
LCM of 2 and 7 = 14
In 1 h
Fred's rounds : Liam's rounds : Jack's rounds
14 : 70 : 10
Distance that Jack completed in 1 h = 2.4 km
10 rounds = 2.4 km = 2400 m
1 round = 2400 ÷ 10 = 240 m
Circumference of the circular track = 240 m
Answer(s): (a) 5; (b) 240 m