Chapter A.8, Problem 32AYU

To determine

To find: How long does it take each printer job alone? What is the speed of each printer?

Answer to Problem 32AYU

Karen’s normal walking speed is $4.05$.

Explanation of Solution

Given:

It takes an HP LaserJet M451 dw laser printer 16 minutes longer to complete an 840-page print job by itself than it takes an HP LaserJet CP4025 dn to complete the same job by itself. Together the two printers can complete the job in 15 minutes.

Calculation:

$\frac{1}{t}+\frac{1}{t+16}=\frac{1}{15}$. $\left(t+16+t\right)\left(15\right)=t^2+16t$

Therefore $t^2+14t-240=0$.

So the roots are $\left(t-10\right)\left(t+24\right)=0$.

$t=10$ faster printer.

$t=26$ slower printer.