Question

it takes one printer, working alone, 9 h longer to print a payroll than it takes a second printer. working together, the printers can print the payroll in 6 h. how long would it take each printer, working alone, to print the payroll?

Answer 1

The second printer would take 24 hours and the first printer would take 33 hours to print the payroll.

Step-by-step explanation:

Let's assume that it takes the second printer, working alone, x hours to print the payroll. According to the given information, it takes the first printer, working alone, 9 hours longer than the second printer to print the payroll. Therefore, the first printer takes x + 9 hours to print the payroll.

When the printers work together, they can print the payroll in 6 hours. We can set up the equation: 1/(x + 9) + 1/x = 1/6 (as the rate of work is inversely proportional to the time).

Multiplying through by the common denominator of 6x(x + 9), we get: 6x + 54 + 6(x + 9) = x(x + 9). Simplifying this equation, we have: 12x = x^2 - 9x - 54.

By rearranging the equation, we get: x^2 - 21x - 54 = 0. Solving this quadratic equation, we find that x = 24 (the negative value is not considered in this case as time cannot be negative).

Therefore, the second printer would take 24 hours and the first printer would take 33 hours to print the payroll.

Answer 2

7.5 Hours (This is questioned weird though so it could be different)

Step-by-step explanation:

Just add 9 to 6 and you'll have 15 divided by two equals 7.5.

Or since it takes 6 hours for both, multiply by 2 equals 12