Vincent, Fred and Tommy started walking at the same time from the same starting point round a circular track. Tommy walked in the clockwise direction. Vincent and Fred walked in an anti-clockwise direction. Tommy took 12 min to complete each round. He met Vincent after every 3 minutes. He met Fred after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Tommy complete in 1 h?
- When Tommy and Vincent met again at the starting point after 1 h, Fred had completed 1.5 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Tommy completed in 1 h
= 60 ÷ 12
= 5
(b)
Tommy took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Tommy's distance is the repeated identity.
Make Tommy's distance the same.
Tommy's distance : Vincent's distance
3 : 12 - 3
3 : 9
Tommy's distance : Fred's distance
6 : 12 - 6
6 : 6
Tommy |
Vincent |
Fred |
3x2 |
9x2 |
|
6x1 |
|
6x1 |
6 |
18 |
6 |
The distance of Tommy is the repeated identity.
LCM of 3 and 6 = 6
In 1 h
Tommy's rounds : Vincent's rounds : Fred's rounds
6 : 18 : 6
Distance that Fred completed in 1 h = 1.5 km
6 rounds = 1.5 km = 1500 m
1 round = 1500 ÷ 6 = 250 m
Circumference of the circular track = 250 m
Answer(s): (a) 5; (b) 250 m