Each week, Mr Smith must make copies for his history class. When he uses both the Xerox and the Hewlett packard copiers, the copies take about 30 minutes. If the Xerox copies is broken the job takes about 50 minutes. How long will the job take if the Hewlett packard copier is broken?

The job will take 75 minutes if the Hewlett Packard copier is broken

Step-by-step explanation:

In this question, we are tasked with calculating the amount of time it will the Xerox copier to finish making the copies whilst working alone

First, let the number of copies to make be x

Thus, the rate at which both copiers deliver when working together is x/30 copies per minute

If the Hewlett Packard is working alone, its rate is x/50 copies per minute

Let the time taken for the Xerox copier to complete its work be y minutes. Its working rate is thus x/y copies per minute

When we add the individual working rates, we have the joint working rate.

Hence, mathematically;

x/50 + x/y = x/30

Multiply through by 1/x

1/50 + 1/y = 1/30

1/y = 1/30 - 1/50

1/y = (50-30) / 1500

1/y = 20/1500

20y = 1500

y = 1500/20

y = 75 minutes

Thus, the job will take 75 minutes if the Hewlett Packard copier is broken