It takes an HP LaserJet 1300 laser printer 10 minutes longer to complete a 600-page print job by itself than it takes an HP LaserJet 2420 to complete the same job by itself. Together the two printers can complete the job in 12 minutes. How long does it take each printer to complete the print job alone? What is the speed of each printer?
I know the time to complete the job for the 1300 is 10+x, because x is the time to complete the job for the 2420. I just don't understand what to do next.
Using the given data we have 3 equations: $$s1*(10+t)=600$$ $$s2*(t)=600$$ $$(s1+s2)*12=600$$ You have 3 equations and 3 variables which you can solve for $s1,s2$.
$s1$=Speed of first printer
$s2$=Speed of second printer
The $1^{st}$ equation gives us: $$s1={600\over(10+t)}$$ The $2^{nd}$ equation gives us: $$s2={600\over t}$$
The $3^{rd}$ equation gives us: $$s1+s2=50$$ Hence
$${600\over(10+t)}+{600\over t}=50$$ Solving this gives you $t$.