College algebra

Question

An office contains 2 printers. Printer B takes 12 minutes longer than Printer A to print a monthly report. Using both printers together, it takes 8 minutes to print the report. How long would it take each printer working alone to print the report?

Answer 1

Let R be the speed of Printer A.

 

Printer A prints 1/R of the report in one minute.

So it takes printer A to print the report in R minutes.

 

Since it takes printer B 12 minutes more, it prints

the report in R+12 minutes.

So it's speed is 1/(R+12)

 

Together they print the report is 8 minutes, so working

together their combined speed is 1/8

 

So  1/R + 1/(R+12) = 1/8

 

The common denominator is 8R(R+12)

 

8(R+12) + 8R = R(R+12)

 

8R + 96 + 8R = R^2 + 12R

 

16R + 96 = R^2 + 12R

 

0 = R^2 - 4R - 96

 

0 = (   R    -  12 )( R  +     8   )

 

R+8 = 0 results in negative speeds

 

R-12 = 0 ---> R = 12

 

The speed of printer A is 1/12 of the report per minute,

so it will take printer A 12 minutes to print the report working alone.

 

THe speed of printer b is 1/(12+12) = 1/24 of the report per minute 

so it will take printer B 24 minutes to print the report working alone.

 

So yes, printer A is twice as fast.

Working together their combined speed is 1/12 + 1/24 = 2/24 + 1/24 = 3/24 = 1/8

so working together they will print the report in 8 minutes, which shows the answers are correct,

as shown in bold above