# Very hard problems about work

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1. May 24, 2015

### Kamakiri

Do you have very hard problems about work? I referred to my algebra book and googled in vain. Not talking about the product of the force magnitude and the displacement magnitude. This is what I’m talking about – Jennifer takes 4 hours to do a job. John takes 6 hours to do the same job. Working together, how many hours will it take them to do the job?

2. May 24, 2015

### Mentallic

So we can think of doing a job as the work rate multiplied by the time taken to finish. In variables, you could use something like this

For Jennifer:
$$4w_1=J$$

For John:
$$6w_2=J$$

So then, we know what w1 and w2 are in terms of the total job J, and now we want to know how long J will take to complete given that they worked together, i.e. the work rate would be the sum of their rates, hence w1+w2. So you simply need to find the value of t in the equation

$$t(w_1+w_2)=J$$

3. May 24, 2015

### Kamakiri

For fear that I was vague, I’m looking for very hard problems. The problem I gave was so easy.

4. May 24, 2015

### Mentallic

Oh, I see. Have you looked into optimization problems?

5. May 24, 2015

### Kamakiri

Yes, can’t find any.

Last edited: May 24, 2015
6. May 24, 2015

### Staff: Mentor

Most algebra textbooks have problems of this sort.

7. May 24, 2015

### Kamakiri

I referred to 2 algebra books. I found easy problems only.

8. May 24, 2015

### Staff: Mentor

That's a pretty small sample. I have seen problems of the type you're looking for in a number of algebra textbooks. Are you looking at college algebra textbooks? These types of questions would be in chapters that deal with rational equations.

9. May 24, 2015

### Stephen Tashi

Are you looking for hard problems in order to prepare for an exam? Or are you actually interested in the subject of real world problems that involve rates of performing tasks?

10. May 24, 2015

### Kamakiri

Yes.

It’s okay if the problem isn’t purely algebraic as long as it’s very hard. I found a problem that involved probability and work, but it was a bit vague, so I neglected it.

It’s not for a test. I’m interested in real-world problems. More importantly, I want very hard problems since I’ll add those to my collection. All I have right now are easy ones.

11. May 24, 2015

### Staff: Mentor

Do a web search with "algebra work problems" as your search string. I did this and got a lot of hits of the type of problem you're looking for.

12. May 24, 2015

### Kamakiri

Those problems were so easy.

By the way, it’s okay if the problem involves differential equations or other branches of math.

13. May 24, 2015

### Staff: Mentor

Then you're going to have to be more specific about what you mean by "very hard problems." In your first post, you said this:
This type of problem is one that is typically presented in a college algebra course, so I suggested that you look at algebra textbooks and examples posted online.

The type of problem you gave is not one that appears in conjunction with differential equations (that I recall), although problems that involve mixtures of liquids coming into and leaving a tank are presented in a course on differential equations.

So what exactly are you looking for?

14. May 24, 2015

### Kamakiri

I mentioned that problem in my first post to clarify what I meant by work. I was just emphasizing that I wasn’t referring to the work in physics. I’m not looking for specific work problems, just for very hard ones. Sadly, I don’t have an example.

A few days ago, I googled “difficult work problem.” I found this:

It takes machine A x hours to manufacture a deck of cards that machine B can manufacture in 1/x hours. If machine A operates alone for y hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously?

Among all the work problems I encountered, which were easy, that was one of the most advanced. Can’t find problems much harder than that.

15. May 24, 2015

### Staff: Mentor

"Difficult work problems" is subjective. A problem that might be difficult for one person could be very easy for someone else. It might be helpful if you said why you're looking for problems like these.

16. May 24, 2015

### PWiz

Have you tried looking at some postgraduate level classical physics textbooks? The problems involving work at that level are multistage questions and are quite complex.

17. May 24, 2015

### Kamakiri

Right. That’s why even if I see easy problems that are marked hard, I don’t mind.

Not yet. Can you point me in the right direction please?

18. May 24, 2015

### PWiz

I'm afraid the best I can do is point you to a google search on what I mentioned. That in turn will point to much better things. There are plenty of free pdfs on the net as well, but my eyes aren't privy to the information they might contain as of yet (to be frank, postgrad texts are out of my league for now, and I don't really have any good references on them).