Jenson, George and Valen started walking at the same time from the same starting point round a circular track. Valen walked in the clockwise direction. Jenson and George walked in an anti-clockwise direction. Valen took 6 min to complete each round. He met Jenson after every 3 minutes. He met George after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Valen complete in 1 h?
- When Valen and Jenson met again at the starting point after 1 h, George had completed 1.2 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Valen completed in 1 h
= 60 ÷ 6
= 10
(b)
Valen took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Valen's distance is the repeated identity.
Make Valen's distance the same.
Valen's distance : Jenson's distance
3 : 6 - 3
3 : 3
Valen's distance : George's distance
5 : 6 - 5
5 : 1
Valen |
Jenson |
George |
3x5 |
3x5 |
|
5x3 |
|
1x3 |
15 |
15 |
3 |
The distance of Valen is the repeated identity.
LCM of 3 and 5 = 15
In 1 h
Valen's rounds : Jenson's rounds : George's rounds
15 : 15 : 3
Distance that George completed in 1 h = 1.2 km
3 rounds = 1.2 km = 1200 m
1 round = 1200 ÷ 3 = 400 m
Circumference of the circular track = 400 m
Answer(s): (a) 10; (b) 400 m