Another Hard Westpac Question Help Please!

[ecyrb]

The country of Big Wally has a railway which runs in a loop 1080 km long. Three companies - A, B and C run trains on the track and plan to build stations. Company A will build three stations equally spaced at 360km intervals. Company B will build four stations at 270km intervals and Company C will build give stations at 216 km.

The government tells them to space their stations so that the longest distance between consecutive stations is as small as possible. What is this distance in kilometers?


I hardly understand the question let alone know how to solve it.
Again any help is appreciated 

[pooshwaltzer]

12*18 = 216km

[ecyrb]

Could you please explain how you did that?

[pooshwaltzer]

A: 3 stations 360km apart
B: 4 stations 270km apart
C: 5 stations 216km apart

LCM = 60 ... 1080/60 = 18

A: 360/18 = 20 ... 20 / 40 / 60
B: 270/18 = 15 ... 15 / 30 / 45 / 60
C: 216/15 = 12 ... 12 / 24 / 36 / 48 / 60

Largest dist is btn 4th station of C and terminal station for A/B/C.
This is (60-48)*18=216km

[_avO]

Was that last years paper? Because I remember doing that question and I QQed