PROBLEM
A circular field has a circumference of 360km .Three cyclists start together and can cycle 48,60,and 72 km a day round the field .When will they meet again?
SOLUTION
Use the cyclists km/day rates to create a diagram
Cyclist 1, 72 km/day, ♦ : takes 5 days to complete 1 lap
Cyclist 2, 60 km/day, ♥ : takes 6 days to complete 1 lap
Cyclist 3, 48 km/day, ♣ : takes 7.5 days to complete 1 lap
Each cyclist's progress is represented by the respective symbol
Notice that each cyclist's progress is represented by a linear graph
Distance
Marker, km
360| ♦ ♥
348|
336|
324|
312|
300| ♥
288| ♦ ♣
276|
264|
252|
240| ♥ ♣
228|
216| ♦
204|
192| ♣
180| ♥
168|
156|
144| ♦ ♣
132|
120| ♥
108|
96| ♣
84|
72| ♦ ♦
60| ♥
48| ♣
36|
24|
12|
0|---------------------------------------------------
Days 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16...
Extending each graph, with each cyclist beginning at the zero marker after completing a lap, puts all the cyclists at the same point again after 30 days.