Solving Work Problems: Algebra Techniques for Jennifer and John

[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?

 

[Mentallic]

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?

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

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

 

[Kamakiri]

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

 

[Mentallic]

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

 

[Kamakiri]

Yes, can’t find any.

 

[Mark44]

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?

Most algebra textbooks have problems of this sort.

 

[Kamakiri]

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

 

[Mark44]

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

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.

 

[Stephen Tashi]

Do you have very hard problems about work?

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?

 

[Kamakiri]

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.

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.

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?

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.

 

[Mark44]

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.

 

[Kamakiri]

Those problems were so easy.

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

 

[Mark44]

Those problems were so easy.

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

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 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?

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?

 

[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.

 

[Mark44]

"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.

 

[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.

 

[Kamakiri]

"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.

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

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.

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

 

[PWiz]

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

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).