Review Contents

Work Problem
Are you familiar with this? A can complete a job in 5 hours while B can do the same job (under the identical conditions blah blah...) in 2 hours. How long will it take the two persons to complete the job when they work together?
This is a very typical example of a work problem though its application can be a bit more complicated. Let’s begin with the basic (and the only) formula
        Assuming       A can do a job (whatever) in time                                s        (seconds, minutes, hours, days ....)
                                 B can do the same  job in time                                       r        (in the same unit as that of A)
                                 If A and B do the job together, they will make it in    t       (unit the same as the above)
                                  
                                Formula                                                            

            The formula looks easy enough. However, if you find quite a straight question, like the example above,  later, let say, from question No 3,  it is certainly either that you are facing a research question or that the computer doesn’t think you’re smart enough. So let’s talk about it in more complicated aspects. But first of all, if you cannot answer the above question, it is like this

    1/t = 1/5 + 1/2        
       t = 7/10 hour

Implications:
1. Beware of units of time. It’s really easy to make a fatal error (by a trap set by the problem author). If you face such a type of question, just change the unit to be the same, probably as that the question is looking for itself. For example, if the final unit in the choice is hour, convert all foreign units to hour. Quite obvious


2. What if the question involves just a fraction of the job itself? Remember that the formula is for a completed job. But, in a very common sense, whenever you can find how long it takes to complete a job, it will takes a proportional period of time to complete a fraction of the job. According to the example, how long will it take the two to complete 1 and a half job?
                     Answer:                                                     7/10 x 1.5 = 21/10 hours.


3. 4 persons are working together, what’s the generalized formula? Easy. The formula can be generalized to whatever the number of persons/machines/pipes...
                                                                    

4. In contrary, two pipes are pumping water into a pond but the third one is pumping the water out, is it that easy just to subtract the third one? Absolutely, yes. In such case, your formula will look like this:
                                                                      

5. The problem gives a specific number of jobs, for example, a machine can produce 500 bottles in 3 minutes. What will the equation look like? If you understand its implication, for instance 1/t or 1/r, 1 is for one job. Therefore, if you have a number of jobs. just replace “1” with it. Referring to our example, if it says instead that A can wash 200 bottles in 5 hours and B can do 500 bottles in 2 hours. If they both spend 10 hours washing bottles, how many can they do?
    Notice that this time the problem doesn’t ask the time but the number of jobs (bottles) instead. The formula always works:
                                                                                x/10 = 200/5 + 500/2
    Hopefully, you can get x (the number of bottles) very easily.

6. Just a very common sense. Time to complete a job when persons/machines etc. work together is always less than the least time used by either of them alone. In the example above if you know nothing to do, a choice that gives an answer from 2 hours is certainly wrong. (A can do it it 5 hrs while B in 2. A result, they both must take less than 2 hrs to do the same job together).

There are more implications of work problems but the above implications will absolutely help you. Let’s practice.