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

4 packs of water and 7 packs of candy bars

step-by-step explanation:

35x4=140

140/20=7

a mantle plume is an upwelling of abnormally hot rock within the earth's mantle. as the heads of mantle plumes can partly melt when they reach shallow depths, they are thought to be the cause of volcanic centers known as hotspots and probably also to have caused flood basalts.

step-by-step explanation: