Let's call T the total amount of material needed to print all the class schedules.
If the first printer takes 15 hours to finish printing all the schedules, that means it prints
[tex]\frac{T}{15}[/tex]of the material per hour.
Similarly, since the second printer takes 9 hours to print all the material, then it prints
[tex]\frac{T}{9}[/tex]of the material per hour.
We con now propose an equation that will allow us to know how fast both printers working in tandem will finish printing all the material:
[tex]x(\frac{T}{15}+\frac{T}{9})=T[/tex]where x is the amount of hours it will take to print T. We begin by calulating what's inside the parentheses:
[tex]x(\frac{T}{15}+\frac{T}{9})=x(\frac{3T+5T}{45})=x(\frac{8T}{45})[/tex]we now go back to the equation:
[tex]x(\frac{8T}{45})=T[/tex]Dividing both sides by T,
[tex]\frac{8x}{45}=1[/tex]Multiplying both sides by 45,
[tex]8x=45[/tex]and finally, dividing both sides by 8,
[tex]x=5.625[/tex]To end this question properly, let's remember that an hour has 60 minutes, so
[tex]0.625h=37.5m[/tex]and a minute has 60 seconds, so
[tex]0.5m=30s[/tex]All in all, it will take both printers 5 hours, 37 minutes and 30 seconds to finish printing the material.
