Ahmad, Neave and Sean started walking at the same time from the same starting point round a circular track. Sean walked in the clockwise direction. Ahmad and Neave walked in an anti-clockwise direction. Sean took 12 min to complete each round. He met Ahmad after every 3 minutes. He met Neave after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Sean complete in 1 h?
- When Sean and Ahmad met again at the starting point after 1 h, Neave had completed 2.1 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Sean completed in 1 h
= 60 ÷ 12
= 5
(b)
Sean took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Sean's distance is the repeated identity.
Make Sean's distance the same.
Sean's distance : Ahmad's distance
3 : 12 - 3
3 : 9
Sean's distance : Neave's distance
6 : 12 - 6
6 : 6
Sean |
Ahmad |
Neave |
3x2 |
9x2 |
|
6x1 |
|
6x1 |
6 |
18 |
6 |
The distance of Sean is the repeated identity.
LCM of 3 and 6 = 6
In 1 h
Sean's rounds : Ahmad's rounds : Neave's rounds
6 : 18 : 6
Distance that Neave completed in 1 h = 2.1 km
6 rounds = 2.1 km = 2100 m
1 round = 2100 ÷ 6 = 350 m
Circumference of the circular track = 350 m
Answer(s): (a) 5; (b) 350 m