Final answer:
To find the number of minutes John would take to print 36 copies with both printers, the equation is t = 36 / (16/5 + 4), where t is the time in minutes.
Step-by-step explanation:
The student asks for an equation to find the number of minutes, t, John would take to make 36 copies using both his HP printer and Epson printer together. To approach this, we must consider the printing rates of both printers and set up the equation accordingly.
The HP printer can print 16 copies in 5 minutes which is a rate of 16/5 copies per minute. The Epson printer can print 4 copies in 1 minute. Combined, the printers can make 16/5 + 4 copies in one minute. Together they print (16/5 + 4)t copies in t minutes.
The equation representing the total number of copies made in t minutes by both printers together is:
(16/5 + 4)t = 36
To solve for t, we would divide both sides of the equation by the combined printing rate of both printers, giving us:
t = 36 / (16/5 + 4)