SOLUTION: Jane wants to buy a photocopier. The sales person has the following information on three models. If all three are used, a specific job can be completed in 50 minutes. If copier A o

COPIER    RATE unit job per minutes

A          1/a
B          1/b
C          1/c
A+B+C      1/a+1/b+1/c

Let x = rate of work of the copier A in units ;
    y = rate of work of the copier B -------- " -----------;
    z = rate of work of the copier C -------- " -----------.

So, my x = 1/a, my y = 1/b and my z = 1/c of the other tutor.

As the condition says, if all three copiers work, the job is done in 50 minutes: 50x + 50y + 50z = 1.

If copier A operates for 20 minutes and copier B operates for 50 minutes, then one-half the job can be is completed.
It means 20x + 50y = .

If copier B operates for 30 minutes and copier C operates for 80 minutes, then three-fifths of the job can be completed.
It means 30y + 80z = .

So you have three equations for three unknowns:

50x + 50y + 50z = 1,      (1)
20x + 50y        = ,    (2)
      30y  + 80z = .    (3)

Notice, this system is LINEAR !!!!!

Now, to solve it, I will do this TRICK.

   1. Add equations (2) and (3) (both sides). You will get

      20x + 80y + 80z = .    (4)      ( <---  = ).

   2. Multiply equation (1) by 8, multiply equation (4) by 5 and write them one under the other, like this:

      400x + 400y + 400z = 8,    (5)
      100x + 400y + 400z = .   (6)

   3. What to do next?  But of course, distract (6) from (5). You will get

      300x = 8 -  =  = .

      Hence, x =  = .  It is the rate of work of the copier A.


Almost all is done. Now from equation (2) you can easily find "y" and from equation (3) find "z".

Please complete these calculations and complete the solution on your own.

The lesson you should learn from this solution is this:

When solving a non-standard joint-work problem, double think which variable to choose as an unknown:  the-time-to-complete-the-job  OR  the rate-of-work.