Question

Three workers are working to cut the trees. Worker X can cut atree every 16 min, Worker Y every 32 min and Worker C every24 min. If they start cutting three trees at the same time at 7:48,at what time will they start cutting trees at the same timeagain?

Answer 1

Given:-

Worker x can cut a tree every 16 min.

Worker y can cut a tree every 32 min.

Worker c can cut a tree every 24 min.

They all three started cutting the tree at the same time 7:48.

To find:-

When will they start cutting trees at the same time again.

At first we need to find the Least common multiple (L.C.M) of the given number 16,32,24.

Prime factorization of 16 is,

`16=2*2*2*2`

Prime factorization of 32 is,

`32=2*2*2*2*2`

Prime factorization 24 is,

`24=2*2*2*3`

So the L.C.M of 16,32,24 is,

So this 96 denotes 96 minutes.

So we need to add 96 minutes to 7:48. For that we first convert 96 minutes to hours.

`96\text{ Minutes =1 hour and 36 minutes}`

So now we need to add 1 hour 36 minutes to 7:48. we get,

`7\colon48+1\colon36=9\colon24`

So they will start cutting the trees together at 9:24.