# Thread: alternative way to solve work problem (thinking the t was a 1--presbyopia rampans)

1. ## alternative way to solve work problem (thinking the t was a 1--presbyopia rampans)

Bill can do a job in 20 mins. Jim can do same job in 30 mins. How long would it take if they worked together? the solution that my author gives is: t/20 + t/30 = 1, with t being the time the job would take with both working together.

I, thinking the t was a 1--presbyopia rampans--set it up thus: 1/20 +1/30 = 1. I proceeded thus: 3/60 + 2/60 = 1 =5/60 (and here I veered sharply off the beaten path and instead of trying to make 5/60 = 1, I divided 60 by 5 and lo! I got 12 which happens to be the correct answer. I used this same approach with numerous other problems in this format and it always came out right. So...to solve this type of problem take the reciprocal of the time it takes for a to do the work, add it to the time it takes b, and then divide the denominator of the result by the numerator and Bob's your uncle!

Am I wrong here?

2. It is the same. What steps would you take if you used the 't'?

The ONLY difference is the author's version allows the notation to help you.

Truthfully, you're just playing like there isn't a 't' in there. The fact that you achieved 5/60 = 1 should suggest to you that something is wrong, not that you invented a new methodology. You had to save it by magic at the end.

3. Originally Posted by tkhunny
It is the same. What steps would you take if you used the 't'?

The ONLY difference is the author's version allows the notation to help you.

Truthfully, you're just playing like there isn't a 't' in there. The fact that you achieved 5/60 = 1 should suggest to you that something is wrong, not that you invented a new methodology. You had to save it by magic at the end.
Well, yes, it did. I didn't really set out to develop anything new. As I say, I thought I was following the authors lead. I misread the small t for a one (1). The fact remains that the formula I stumbled upon and outlined works. I'm sure it isn't new...I am not a mathematician or anything like one. Still, I find it interesting to fool around....sometimes you come up with something useful...at least to you. As I say, I know it isn't new...but it is new to me!

4. Originally Posted by tkhunny
It is the same. What steps would you take if you used the 't'?

.
I would have done it thus: t/20 +t/30 = 1. I would eventually have come to 3t + 2t= 60. and 60/5 = 12.

5. You're missing my point. It isn't new or useful - even to you. It's wrong. 5/60 = 1 should tip you off.

6. Originally Posted by tkhunny
You're missing my point. It isn't new or useful - even to you. It's wrong. 5/30 = 1 should tip you off.
No. 5/30 means nothing to me I this context. The problem was this: Bill did the job in 20 mins and Jim did it in 30. How long does it take to do it together. The way my author would set it up is this: t/20 + t/30 = 1 The way I put it was this:1/20 + 1/30 =1. I saw very early on that this equation was not going to work so, for fun I tried something else, namely dividing the numerator of the result of adding 1/20 with1/30 into the denominator. And in so doing I got 12. Where do you get 5/30? In neither the author's approach or my stumbling one did 5/30 make any appearance.

7. Originally Posted by allegansveritatem
No. 5/30 means nothing to me I this context. The problem was this: Bill did the job in 20 mins and Jim did it in 30. How long does it take to do it together. The way my author would set it up is this: t/20 + t/30 = 1 The way I put it was this:1/20 + 1/30 =1. I saw very early on that this equation was not going to work so, for fun I tried something else, namely dividing the numerator of the result of adding 1/20 with1/30 into the denominator. And in so doing I got 12. Where do you get 5/30? In neither the author's approach or my stumbling one did 5/30 make any appearance.
I think he meant 5/60, which showed up in the OP, "3/60 + 2/60 = 1 =5/60". The point is that writing nonsense is dangerous, even when you know it is nonsense.

I presume you realize that the 5/60 you get here is the reciprocal of the answer; that is because the rates 3/60 and 5/60 add up to give a combined rate of 5/60 = 1/12 jobs per minute, and the time (minutes per job) is the reciprocal of that. What you did was to divide the bottom by the top, which is just what the reciprocal means. This is why your work happened to be correct.

The right thing to do when you come up against something that doesn't make sense is not to "for fun try something else" at random, but to think about what that thing you wrote does mean, so you can make sense of it, and then find something sensible to do. Without understanding, you are more likely to come up with a wrong answer than a right one; and you'll never know which it is!

Yes, what you did turned out to be a "method" you could follow to get correct answers to problems that are exactly like this one. But when you learn algebra, the point is not to master a particular problem; it is to learn techniques by which you can solve problems you've never seen before, because you understand how they work.

8. Originally Posted by Dr.Peterson

Yes, what you did turned out to be a "method" you could follow to get correct answers to problems that are exactly like this one. But when you learn algebra, the point is not to master a particular problem; it is to learn techniques by which you can solve problems you've never seen before, because you understand how they work.
I hear you. I don't know enough to fool around profitably. It reminds me of what Delacroix said: Great painters learn the rules of art thoroughly and then forget about them. Bad painters never learn the rules to the point where they can afford to forget them. Or something to that effect.

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