Question

Printers A and B work together to complete an assigned job. Printer A completes this job in 8 hours. Both printers working together complete the job in 6 hours. How many hours does it take for Printer B to complete the job if it was working alone?

a) 8
b) 12
c) 16
d) 24

Answer 1

To calculate the time it takes for Printer B to complete the job working alone, we set up an equation based on their work rates. Printer A's work rate is 1/8, and their combined rate is 1/6. Solving for Printer B's rate reveals it takes Printer B 24 hours to complete the job alone.

Step-by-step explanation:

To find out how long it takes for Printer B to complete the job working alone, we can use the concept of work rate. Printer A completes the job in 8 hours, which means its work rate is 1/8. When Printer A and B work together, they complete the job in 6 hours, so their combined work rate is 1/6. The work rate of Printer B can be found by subtracting Printer A's rate from the combined rate of both printers.

Let's assume Printer B alone takes x hours to finish the job. Then Printer B's work rate would be 1/x. The equation based on their combined work rate is:

1/8 + 1/x = 1/6

To solve for x, we find a common denominator and get:

(x + 8)/(8x) = 1/6

After multiplying both sides by 8x and then by 6 to clear the denominators, we have:

6x + 48 = 8x

Subtracting 6x from both sides, we get:

48 = 2x

So, x = 48/2 = 24.

Therefore, it takes Printer B 24 hours to complete the job working alone, which corresponds to option d).