John, Lee and Riordan started walking at the same time from the same starting point round a circular track. Riordan walked in the clockwise direction. John and Lee walked in an anti-clockwise direction. Riordan took 12 min to complete each round. He met John after every 2 minutes. He met Lee after every 7 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Riordan complete in 1 h?
- When Riordan and John met again at the starting point after 1 h, Lee had completed 2.3 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Riordan completed in 1 h
= 60 ÷ 12
= 5
(b)
Riordan took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Riordan's distance is the repeated identity.
Make Riordan's distance the same.
Riordan's distance : John's distance
2 : 12 - 2
2 : 10
Riordan's distance : Lee's distance
7 : 12 - 7
7 : 5
Riordan |
John |
Lee |
2x7 |
10x7 |
|
7x2 |
|
5x2 |
14 |
70 |
10 |
The distance of Riordan is the repeated identity.
LCM of 2 and 7 = 14
In 1 h
Riordan's rounds : John's rounds : Lee's rounds
14 : 70 : 10
Distance that Lee completed in 1 h = 2.3 km
10 rounds = 2.3 km = 2300 m
1 round = 2300 ÷ 10 = 230 m
Circumference of the circular track = 230 m
Answer(s): (a) 5; (b) 230 m