Tim, Jenson and Jeremy started walking at the same time from the same starting point round a circular track. Jeremy walked in the clockwise direction. Tim and Jenson walked in an anti-clockwise direction. Jeremy took 6 min to complete each round. He met Tim after every 2 minutes. He met Jenson after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Jeremy complete in 1 h?
- When Jeremy and Tim met again at the starting point after 1 h, Jenson had completed 2.4 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Jeremy completed in 1 h
= 60 ÷ 6
= 10
(b)
Jeremy took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Jeremy's distance is the repeated identity.
Make Jeremy's distance the same.
Jeremy's distance : Tim's distance
2 : 6 - 2
2 : 4
Jeremy's distance : Jenson's distance
4 : 6 - 4
4 : 2
Jeremy |
Tim |
Jenson |
2x2 |
4x2 |
|
4x1 |
|
2x1 |
4 |
8 |
2 |
The distance of Jeremy is the repeated identity.
LCM of 2 and 4 = 4
In 1 h
Jeremy's rounds : Tim's rounds : Jenson's rounds
4 : 8 : 2
Distance that Jenson completed in 1 h = 2.4 km
2 rounds = 2.4 km = 2400 m
1 round = 2400 ÷ 2 = 1200 m
Circumference of the circular track = 1200 m
Answer(s): (a) 10; (b) 1200 m