A worker can clean a pool in four hours less time than it takes another worker. If men work together, the job takes 8/3 hours. How long would it take the slower man working alone?

<h3>What is the hour(s) that will take the slower man?</h3>

Taking x to be the hour(s) for the slower man and (x-4) be the number of hours for the faster man working separately. Thus,

1/x+1/(x-4)=1/8/3

1/x+1/(x-4)=3/8

[(x-4)+x]=(x)(x-4)(3/8)

2x-4=(x^2–4x)(3/8)

16x-32=3x^2–12x

3x^2–28x+32=0

<h3>Factorisation</h3>

Factorise to solve the value of x:

There are 2 values of x for the factors: (3x-4)(x-8) =0

3x - 4 =0; 3x= 4; x = 4/3 or 1 1/3 hours (invalid due to the fact that it fits not for the slower man who will work alone for 4 hours slower than the faster man as it is only 4/3 hours which is lesser than 4 hours.
x - 8 = 0; x = 8 hours (answer to be adopted because it is fit for the slower man to do the job separately for 4 hours lesser than the faster man.

Verify:

1/8 + 1/(8–4) = 1/8/3 =3/8

1/8 + 1/4 = 3/8

(1+2)/8 = 3/8

3/8 = 3/8

Therefore, the correct answer is x = 8 hours for the slower man to work alone.

learn more about factorisation: brainly.com/question/25829061

#SPJ1

7 0

2 years ago