help me please?

Question

A company owns 15 machines that produce pens. When all machines are operating, 54000 pens are produced in 6 hours.
On a particular day, 69000 pens must be produced but 7 of the machines are not working.
Assuming the rest of the machines continue to work at the same rate, how many hours must they operate in order to meet the target?

Answer is 14 3/8

Please show workings..cos this question is very confusing...

Answer 1

54000 pens in 6 hours by 15 machines
--> 9000 pens per hour by 15 machines
--> 600 pens per hour by 1 machine.

69000 pens must be produced with 8 machines.
8 machines produce 4800 pens per hour.

So, no. of hours = 69000/4800 = 690/48 = 115/8 = 14 3/8

Answer 2

Machines Hours Pens
8 x 69000
15 6 54000

"Machines" and "Hours" have an INDIRECT relationship, "Machines" and "Pens" have a DIRECT relationship. So, writing the above information in equation form gives:

8/15 = (6/x) * (69000/54000)

(I assume you are aware of how I arrived at this.)

8/15 = (6/x) * 23/18
6/x = (8/15) * (18/23)

6/x = 48/115
x = (115/48) * 6

x = 14 3/8

Therefore, the remaining 8 machines should work for 14 3/8 hours to produce 69000 pens.

Answer 3

15 machines can produce 54000/6 = 9000 pens per hour. One machine can produce 9000/15=600 pens per hours. If 7 are not working that means 8 are. 8*600=4800 pens can be produced per hour. 69000/4800=14 3/8 hours to meet order.