Question

A rectangular field has dimensions 100m by 80m. Three cyclists start together and can cycle 24m, 30m and 36m per minute, round the field. After how many days will they meet again at the starting point?

Answer 1

they will meet after travelling a particular distance the distance will be LCM of the distances ...
that will be = 360 m.
so when they all travel sixty meters then the LCM of the time is then when they meet...
thus traveller 1 ----- 15 minutes
traveller 2 ------- 12 minutes
traveller 3 -------- 10 minutes.
therefore after 60 minutes they will meet again....

Answer 2

They will meet again at the distance of LCM of 24,30,36 meters with respect to the rectangle.

24 = 2×2×2×3
30 = 2×3×5
36 = 2×2×3×3

LCM = (2×2×2)×(3×3)×5
= 8×9×5
= 360 m

Perimeter of the rectangle
= 2(l+b)
= 2(100+80)
= 360 m

360/360 = 1

Therefore the three cyclists will again meet at the starting point only.

Hence the distance covered by then will be multiple of 360 i.e 360,720,1080 m

Time required for each cyclist to reach again the starting point

1. 24m/min
t = 360/24 = 15 min

2. 30 m/min
t = 360/30 = 12 min

3. 36 m/min
t = 360/36 = 10 min
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Therefore the time at which they will meet again will be LCM of 15,12,10

15 = 3×5
12 = 2×2×3
10 = 2×5

LCM = (2×2)×(3)×(5)
= 60 min

Time
= 60 min
= 1 hr
= (1/24) Days