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

43

step-by-step explanation:

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?