Question

The weekly news magazine has a big story naming the Person of the Year and the editor wants the magazine to be printed as soon as possible. She has asked the printer to run an extra printing press to get the printing done more quickly. Press #1 takes 6 hours more than Press #2 to do the job and when both presses are running they can print the job in 4 hours. How long does it take for each press to print the job alone?

Short answer

The number of hours needed to complete the job for Press #1 is 12 hours and for Press #2 is 6 hours.

Step-by-step solution

Step 1. Given information

Press #1 takes 6 hours more than Press #2 to do the printing job. Both presses together can print the job in 4 hours. Find how long does it take for each press to print the job alone.

Step 2. Calculation

Consider x be the number of hours needed to complete the job for Press #2.

So, the number of hours needed to complete the job for Press #1 is $x+6$.

Form a table using given the information-

	Number of hours needed to complete the job	Part of job completed/hour
Press#1	$x+6$	$\frac{1}{x+6}$
Press#2	x	$\frac{1}{x}$
Together	4	role="math" localid="1645078934228" $\frac{1}{4}$

Amount of work completed together can be written by,

role="math" localid="1645079254616" $\frac{1}{4}=\frac{1}{x}+\frac{1}{x+6}$

Step 3. Solve the equation

LCD of denominator is $4x\left(x+6\right)$.

Multiply both sides by the LCD.

$\left(4x\left(x+6\right)\right)\frac{1}{4}=\left(4x\left(x+6\right)\right)\left(\frac{1}{x}+\frac{1}{x+6}\right)$

Simplify the equation

$$\begin{gathered} x\left(x+6\right)=4\left(x+6\right)+4x \\ {x}^2+6x=4x+24+4x \end{gathered}$$

Combine like terms

$x^2-2x-24=0$

Solve the quadratic equation

$\left(x-6\right)\left(x+4\right)=0$

So,

$x-6=0\Rightarrow x=6$

$x+4=0\Rightarrow x=-4$

Number of hours can not be negative.

So, the number of hours needed to complete the job for Press #2 is 6 hours.

The number of hours needed to complete the job for Press #1 is $6+6=12$hours.