# Story problem (math) **URL:** \ **Category:** Factual Questions\ **Created:** [June 15, 2021, 4:25pm UTC](https://boards.straightdope.com/t/story-problem-math/944334 "2021-06-15T16:25:43Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Oly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/oly/32/8255_2.png) [@Oly](https://boards.straightdope.com/u/Oly)\ **Post date:** [June 15, 2021, 4:25pm UTC](https://boards.straightdope.com/t/story-problem-math/944334/1 "2021-06-15T16:25:43Z")
This seems like it should have a simple solution, but it’s not coming to me. Let’s say three people work in a factory that makes dodads. Person A is assigned to work 95% on dodads and spend 5% of their time on other things. Person B is assigned to work 75% on dodads, and Person C 50% on dodads. Assume everyone makes dodads at the same rate. The question is: For every 100 dodads made, how many will be made by Persons A, B and C, respectively? ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [June 15, 2021, 4:29pm UTC](https://boards.straightdope.com/t/story-problem-math/944334/2 "2021-06-15T16:29:33Z")
This looks _a lot_ like homework, but I’ll give you the benefit of the doubt. It does have a simple solution. Add up the number of hours each spends making doodads and divide by the total. Assuming that they all work the same total number of hours, then in every 100 hours, A will do 95 hours of doodad work, B, 75, and C, 50. That’s a total of 220 hours. So A will make 95/220 % of the doodads, B will make 75/220 %, and C will make 50 / 220%. ---
**Author:** ![Roderick\_Femm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/roderick_femm/32/14875_2.png) [@Roderick\_Femm](https://boards.straightdope.com/u/Roderick_Femm)\ **Post date:** [June 15, 2021, 4:55pm UTC](https://boards.straightdope.com/t/story-problem-math/944334/3 "2021-06-15T16:55:27Z")
In other words, the story problem doesn’t have enough information to answer the question, without making an assumption like iamthewalrus\_3 has done. That’s why OP can’t come up with an answer, there isn’t one as presented. ---
**Author:** ![TroutMan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/troutman/32/6721_2.png) [@TroutMan](https://boards.straightdope.com/u/TroutMan)\ **Post date:** [June 15, 2021, 5:10pm UTC](https://boards.straightdope.com/t/story-problem-math/944334/4 "2021-06-15T17:10:25Z")
Of course there is. The problem says **for every 100 doodads**. The assumption about working 100 hours is just to make it easier to think about it, but the percentage each contributes to the total output is independent of that. A: 95/220 = 43% → 43 doodads B: 75/220 = 34% → 34 doodads C: 50/220 = 23% → 23 doodads ---
**Author:** ![Oly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/oly/32/8255_2.png) [@Oly](https://boards.straightdope.com/u/Oly)\ **Post date:** [June 15, 2021, 5:41pm UTC](https://boards.straightdope.com/t/story-problem-math/944334/5 "2021-06-15T17:41:55Z")
Ok, thanks. Simple indeed. I’d figured this out before and am embarrassed to have asked for help but was having an aggravating mental block. Thanks for the assist. And I promise it’s not homework. I’m at the other end of the lifeline (which probably explains the mental block) ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [June 15, 2021, 9:14pm UTC](https://boards.straightdope.com/t/story-problem-math/944334/6 "2021-06-15T21:14:13Z")
> [@TroutMan](#): > > Of course there is. The problem says **for every 100 doodads**. The assumption about working 100 hours is just to make it easier to think about it, but the percentage each contributes to the total output is independent of that. > > A: 95/220 = 43% → 43 doodads > B: 75/220 = 34% → 34 doodads > C: 50/220 = 23% → 23 doodads IMO Nope. Try this: Person A works 1 hour per year. person B works 1 hour per month. Person C works 40 hours per week. If it takes 5 worker-minutes to make a doodad, person C will make all of the first hundred early on Tuesday’s shift. Nobody else will make any. The production percentages are 0% / 0% / 100%. If we wait a full year and then count the doodads made, person A will have worked 95% of 1 hour on doodads and made 11 of them. Person B will have worked 75% of 12 hours = 9 hours and made 9 \* 12 = 108 of them. Person C will have worked 50% of 52 weeks times 40 hours = 1040 hours \* 12 doodads per hour = 12,480 doodads. For a total of 11 + 108 + 12480 = 12,599 doodads made. Of which person C made 12480/23599 or 99.05% of them. Now the exact numbers I chose determine the numerical result I got. Granted. If I choose different numbers of man hours per worker per year I’d get a different fraction of doodads produced. But the fact I get different production _fractions_ depending on which man-hours worked per time period I assume says there’s a missing variable in the original problem. The obvious assumption is that everybody works the same number of hours. But that’s an assumption. I’ve demonstrated that the problem breaks down if that assumption is not respected. ---
**Author:** ![TroutMan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/troutman/32/6721_2.png) [@TroutMan](https://boards.straightdope.com/u/TroutMan)\ **Post date:** [June 15, 2021, 10:03pm UTC](https://boards.straightdope.com/t/story-problem-math/944334/7 "2021-06-15T22:03:17Z")
If three people “work in a factory” and “they make doodads at the same rate” in a story problem, it is a safe assumption that they work the same hours. Saying that “well, person A has a job that’s only 1 hour per year” is the kind of gotcha that you play in elementary school, not in an actual problem. ---
**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\ **Post date:** [June 16, 2021, 12:36am UTC](https://boards.straightdope.com/t/story-problem-math/944334/8 "2021-06-16T00:36:36Z")
Yeah, everyone works equal hours is not a big assumption for a job. Particularly since it was specified how much of their time each person spent on the task. If they worked different number of hours, then why bother telling us what proportion of the time the spent working on a particular project. It’s a non-sequitur. The big assumption is that they all make doodads at the same rate. But that was specified to be true in the OP. ---
**Author:** ![Kron](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kron/32/12444_2.png) [@Kron](https://boards.straightdope.com/u/Kron)\ **Post date:** [June 16, 2021, 12:42am UTC](https://boards.straightdope.com/t/story-problem-math/944334/9 "2021-06-16T00:42:44Z")
Nitpick: unless I’ve suddenly started rewriting history in my head, I do believe that our wildly unnecessary embargo on homework help was lifted some time ago. ---
**Author:** ![Nars\_Glinley](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/nars_glinley/32/8177_2.png) [@Nars\_Glinley](https://boards.straightdope.com/u/Nars_Glinley)\ **Post date:** [June 16, 2021, 1:59am UTC](https://boards.straightdope.com/t/story-problem-math/944334/10 "2021-06-16T01:59:24Z")
It’s still listed as a no-no in the registration agreement. Admittedly, it hasn’t been updated in 3 years. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [June 16, 2021, 2:49am UTC](https://boards.straightdope.com/t/story-problem-math/944334/11 "2021-06-16T02:49:17Z")
Okay, let me take a shot at this without reading the other posts. Let’s assume A, B, and C could all individually make 100 dodads in X amount of time, if they were working exclusively on making dodads. Giving their other work duties, we know that in X amount of actual work time, A would make 95 dodads, B would make 75, and C would make 50. So in X amount of time, they collectively make 220 dudads, with A making 43% of them, B making 34%, and C making 23% (rounded off to the nearest percent). Applying those same percentages to a total of 100 dodads, we see that A made 43, B made 34, and C made 23. ---
**Author:** ![md-2000](https://avatars.discourse-cdn.com/v4/letter/m/9d8465/32.png) [@md-2000](https://boards.straightdope.com/u/md-2000)\ **Post date:** [June 16, 2021, 3:09am UTC](https://boards.straightdope.com/t/story-problem-math/944334/12 "2021-06-16T03:09:58Z")
Yes, the only proviso is that the problem should have said “they worked the same number of hours” to make the problem concise. “They make dodads at the same rate” really means what we think it perhaps means, then it means “they all make X dodads each hour” depending what they mean by “same rate” and the answer then would be 33.3333 each. Person C can just produce at the same rate as the others per hour while devoting only half his time to actual production. Needs clarity. ---
**Author:** ![don\_t\_ask](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)\ **Post date:** [June 16, 2021, 9:09am UTC](https://boards.straightdope.com/t/story-problem-math/944334/13 "2021-06-16T09:09:49Z")
What puzzles me is, in this day and age, who the hell still uses doodads? ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [June 16, 2021, 9:45am UTC](https://boards.straightdope.com/t/story-problem-math/944334/14 "2021-06-16T09:45:26Z")
Dodads, not doodads. Completely different thing. ---
**Author:** ![bob\_2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bob_2/32/3341_2.png) [@bob\_2](https://boards.straightdope.com/u/bob_2)\ **Post date:** [June 16, 2021, 10:11am UTC](https://boards.straightdope.com/t/story-problem-math/944334/15 "2021-06-16T10:11:54Z")
This may be the answer to this: [Why is the SDMB membership declining, and what’s the best way to add younger members? - About This Message Board - Straight Dope Message Board](https://boards.straightdope.com/t/why-is-the-sdmb-membership-declining-and-whats-the-best-way-to-add-younger-members/944208/33) Let’s have an “Answer your knotty homework Questions” section. ---
**Author:** ![Princhester](https://avatars.discourse-cdn.com/v4/letter/p/3e96dc/32.png) [@Princhester](https://boards.straightdope.com/u/Princhester)\ **Post date:** [June 16, 2021, 12:09pm UTC](https://boards.straightdope.com/t/story-problem-math/944334/16 "2021-06-16T12:09:34Z")
Yeah your doodad is like a thingummy or whatsit if you know what I mean. Whereas a dodad is more like a whosamacallit or whatsamadoodle. That type of thing. See? Actually now that I think about it, it might be the other way around. Hmmmm. Well, anyway, I’m sure you get the general principle, right? ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [June 16, 2021, 2:58pm UTC](https://boards.straightdope.com/t/story-problem-math/944334/17 "2021-06-16T14:58:29Z")
In general, it is perfectly reasonable to have to make an assumption to find an answer. Google the snowplow problem for an example. It was in the book I used when I took differential equations and then dropped from later editions presumably on the basis that problems should not require thought. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 16, 2021, 3:26pm UTC](https://boards.straightdope.com/t/story-problem-math/944334/18 "2021-06-16T15:26:09Z")
OK, I just Googled the [snowplow problem](https://secure.math.ubc.ca/~israel/m215/plows/plows.html). It’s not a good problem, not because it requires assumptions, but because it requires assumptions that are either unreasonable or unfounded. My first assumption, and the one most reasonable in the real world, would have been that the two plows move at the same speed, regardless of the amount of snow in their path. But the problem falls apart under this assumption, because we’re explicitly told that the second plow catches up to the first. So we must assume that the speeds are not equal, and that the second one is faster, presumably as a result of having less snow in its path than the first… but now we need a model for how the speed of a plow depends on the depth of snow. The model that page proposes is that a plow’s speed is inversely proportional to snow depth (i.e., that a plow moves at such a speed as to clear snow at a constant rate), but that’s clearly a flawed model, because it leads to infinitely-fast plows. A proper solution would require a more detailed model, but there isn’t sufficient information to construct any more detailed model. ---
**Author:** ![ArtBeforeScience](https://avatars.discourse-cdn.com/v4/letter/a/73ab20/32.png) [@ArtBeforeScience](https://boards.straightdope.com/u/ArtBeforeScience)\ **Post date:** [June 16, 2021, 6:54pm UTC](https://boards.straightdope.com/t/story-problem-math/944334/19 "2021-06-16T18:54:17Z")
Questions like these keep me unemployed because I can’t answer them in job interviews. My weasel-out-of-it approach would be to just let them go for about 2 weeks, make sure they sign their own dodads, and then count them up at the end of that time. ---
**Author:** ![Delayed\_Reflex](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/delayed_reflex/32/3172_2.png) [@Delayed\_Reflex](https://boards.straightdope.com/u/Delayed_Reflex)\ **Post date:** [June 16, 2021, 7:30pm UTC](https://boards.straightdope.com/t/story-problem-math/944334/20 "2021-06-16T19:30:58Z")
> [@Chronos](#): > > OK, I just Googled the [snowplow problem](https://secure.math.ubc.ca/~israel/m215/plows/plows.html). It’s not a good problem, not because it requires assumptions, but because it requires assumptions that are either unreasonable or unfounded. > > My first assumption, and the one most reasonable in the real world, would have been that the two plows move at the same speed, regardless of the amount of snow in their path. But the problem falls apart under this assumption, because we’re explicitly told that the second plow catches up to the first. So we must assume that the speeds are not equal, and that the second one is faster, presumably as a result of having less snow in its path than the first… but now we need a model for how the speed of a plow depends on the depth of snow. The model that page proposes is that a plow’s speed is inversely proportional to snow depth (i.e., that a plow moves at such a speed as to clear snow at a constant rate), but that’s clearly a flawed model, because it leads to infinitely-fast plows. A proper solution would require a more detailed model, but there isn’t sufficient information to construct any more detailed model. There seem to be variations on the problem - [this one](http://sites.science.oregonstate.edu/~show/docs/256-SnowPlow.pdf) seems to be written a bit better as it defines a snowplow as being able to remove snow at a fixed rate, and there is only one plow. [Next page](https://boards.straightdope.com/t/story-problem-math/944334.md?page=2)