If the Mega-Print 3000 printer can print a large document in one fourth the time of the Super-Print 1000 printer, and the printers working together can print the document in 6 hours, how long would it take the slower printer alone to print the document?

Explanation:

Ignore the values 3000 and 1000 as they are simply labels for the printer names (or brand models). I'll call the two printers A and B for simplicity.

Printer A can produce a large document in 1/4th the time printer B can do the same job. So we can say x = (1/4)y where x and y are the times it takes for both printers to do the job if they work alone. Solving for y gets us y = 4x.

Printer A can do the full job, on its own, taking x hours. It's rate is 1/x jobs per hour. Printer B's rate is 1/y = 1/(4x) jobs per hour for similar reasons.

Their combined rate is

1/x + 1/(4x) = 4/(4x) + 1/(4x) = 5/(4x)

Set this equal to 1/6 and solve for x. The 1/6 represents the combined rate based on how they can work together to get the job done in 6 hours.

5/(4x) = 1/6

5*6 = 4x*1 cross multiply

30 = 4x

4x = 30

x = 30/4 ... divide both sides by 4

x = 7.5

Printer A takes 7.5 hours to do the job alone

y = 4x

y = 4*7.5

y = 30

Printer B takes 30 hours to get the job done if it worked alone

Note how

1/x + 1/y = 1/7.5 + 1/30 = 4/30 + 1/30 = 5/30 = 1/6

so this confirms we have the right answer.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet