Question

A rectangular field has dimensions $100m\times 80m$. 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

First we have to find the LCM of 24, 30 and 36.

$24=2\times 2\times 2\times 330=2\times 3\times 536=2\times 2\times 3\times 3$

LCM = $2\times 2\times 2\times 3\times 3\times 5=360$

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

So, 360/360 = 1

They will only meet at one point which is the starting point.

The distance covered by them will be multiple of 360.

Now find the time

for 1st t=360/24 =15 minute

for 2nd t=360/30= 12 minute

for 3rd t=360/36= 10 minute

Again take the LCM of time in order to find common time

$15=(3\times 5)$, $12=(2\times 2\times 3)$, $10=(2\times 5)$

LCM $=2\times 2\times 3\times 5=60minute$

So the required time will be $60min$, 1 hour or( 1/24) days