100 points

two workers finished a job in 7.5 days. how long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?

It will take the first person 12 days and the second person x+12 or 20 days

Step-by-step explanation:

The equation for time to do a job is

1/A + 1/B = 1/C

where A is the time for person A to do the job alone

B is the time for person B to do the job alone

and C is the time for A and B to do the job together

Person A does it in x days and Person B does it in x+8 days and together they do it in 7.5 days

Substituting in

1/ (x) + 1/ (x+8) = 1/ 7.5

Multiply by (x)(x+8)(7.5) to clear the fractions

(x)(x+8)(7.5)(1/ (x) + 1/ (x+8)) = (1/ 7.5)(x)(x+8)(7.5)

Distribute

(x)(x+8)(7.5)(1/ (x)) +(x)(x+8)(7.5)( 1/ (x+8)) = (1/ 7.5)(x)(x+8)(7.5)

Cancel

(x+8)(7.5) + 7.5x = (x)(x+8)

Distribute

7.5x +60 +7.5x = x^2 +8x

Combine like terms

15x +60 = x^2 +8x

Subtract 15x from each side

15x-15x +60 = x^2 +8x-15x

60 = x^2 -7x

Subtract 60 from each side

60-60 = x^2 -7x - 60

0 = x^2 -7x - 60

Factor

0 = (x-12) *(x+5)

Using the zero product property

x-12=0  x+5=0

x=12   x=-5

Since the number of days cannot be zero

It will take the first person 12 days and the second person x+12 or 20 days

step-by-step explanation: