Eric, Billy and Sam started walking at the same time from the same starting point round a circular track. Sam walked in the clockwise direction. Eric and Billy walked in an anti-clockwise direction. Sam took 6 min to complete each round. He met Eric after every 2 minutes. He met Billy after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Sam complete in 1 h?
- When Sam and Eric met again at the starting point after 1 h, Billy had completed 1.9 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Sam completed in 1 h
= 60 ÷ 6
= 10
(b)
Sam took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Sam's distance is the repeated identity.
Make Sam's distance the same.
Sam's distance : Eric's distance
2 : 6 - 2
2 : 4
Sam's distance : Billy's distance
5 : 6 - 5
5 : 1
Sam |
Eric |
Billy |
2x5 |
4x5 |
|
5x2 |
|
1x2 |
10 |
20 |
2 |
The distance of Sam is the repeated identity.
LCM of 2 and 5 = 10
In 1 h
Sam's rounds : Eric's rounds : Billy's rounds
10 : 20 : 2
Distance that Billy completed in 1 h = 1.9 km
2 rounds = 1.9 km = 1900 m
1 round = 1900 ÷ 2 = 950 m
Circumference of the circular track = 950 m
Answer(s): (a) 10; (b) 950 m