Question

Kent can cut and split a cord of wood twice as fast as Brent can. When they work together , it takes them 4hr. How long would it take each of them to do the job alone

Answer 1

Brent will take 12 hours to do the work alone

Kent will take 6 hours to do the work alone

Explanation:

We can use the formula

W = RT

to solve this.

W is Work Done

R is the Rate at which it is done

T is the Time taken

Now, let Brent's rate be x

and since Kent can to it TWICE as fast, we can say Kent's rate is 2x

Now, to cut and split a cord (let that be "1" unit of work, W = 1 ), together they take 4 hours. So we can write:

W = RT

1 = (x + 2x)(4)

Now, we solve this for x:

`1=(x+2x)(4)\\1=(3x)(4)\\1=12x\\x=(1)/(12)`

This means that 1/12th of work is done in 1 hour, so it will take him "12" hours to do full work alone.

This is Brent.

Kent is TWICE as fast, so he will take HALF THE TIME, that is 6 hours to do the work alone.

Brent will take 12 hours to do the work alone

Kent will take 6 hours to do the work alone