Poorly worded math story problem

[Borg]

I am having a discussion/disagreement on another forum about the interpretation of the story problem below.

"In a department store, with only one girl working on the gift-wrapping service, four gifts per hour were wrapped in the first 15 hours. With help from a colleague for the next 45 hours, the amount of gifts wrapped rose to seven per hour.
How many gifts were wrapped each hour in the last 45 hours only?"

The 'answer' to this is supposed to be 8 which means that they are interpreting "seven per hour" in the second sentence to mean that it is an average for the entire 60 hours.

As I read through the paragraph, the first sentence states a gift wrapping rate that is an hourly rate and also happens to be the total average hourly rate at that point. The second sentence refers to a time period of 45 hours and a rate of seven per hour. However, it does not specify whether that rate was an hourly rate for the 45 hour period or was a total average hourly rate for the entire 60 hour period. Without knowing the question yet, I interpret the phrase "the next 45 hours" as being the object of the stated seven per hour rate. Therefore, I read that to be an average for the 45 hours and not for the entire 60 hours.

To me, this looks like a trick question that's asking for an answer that they give in the second sentence. Most people are stating that the most likely meaning is that "seven per hour" refers to the entire 60 hour period because it makes the most sense based on the question that is asked after that sentence. I have stated that if I change the question being asked in the third sentence, the meaning of the information given in the first two sentences should not change.

"What was the average number of gifts wrapped per hour for the entire 60 hours?"

Should people assume that this question is now a trick question because the 7/hour rate given in the second sentence is an overall rate as many are stating about the original question? Or would the assumption now be that the reader should perform a different calculation because the question is different? If this was the original question, I believe that most of them would have interpreted the information in sentence two differently and considered it a rate for the 45 hour period.

If I'm wrong, I'm wrong. No problem but, I would rather hear this from someone who studies English for a living. Thanks in advance for your time.

 

[Rover_KE]

Welcome to the forum.

Please provide a link to the other forum.

 

[Borg]

Was bored today and searched for a puzzle. Came across this one....

So I am missing something in this one. The answr is 8. Can someone explain? In a department store, with only one girl working on the gift-wrapping service, four gifts per hour were wrapped in the first 15 hours. With help from a colleague for the next 45 hours, the amount of gifts wrapped rose...

www.physicsforums.com

 

[SoothingDave]

I would read the original sentence to mean that 7/hr was the rate for the final 45 hours. It literally says "for the next 45 hours..."

It's a poorly worded question. If they really don't mean that, they need to add an "overall" somewhere or tack on "for the whole 60 hours."

 

[jutfrank]

Without knowing the question yet, I interpret the phrase "the next 45 hours" as being the object of the stated seven per hour rate. Therefore, I read that to be an average for the 45 hours and not for the entire 60 hours.

That's understandable. As you say, the question has two different interpretations.

It isn't meant to be a trick question—it's a mathematical question. I'm pretty sure the person who wrote the puzzle meant that the 7-per-hour rate was for the whole 60 hours. It's imprecisely worded.

 

[emsr2d2]

In my opinion, if they simply wanted the total number of gifts wrapped in the last 45 hours, they wouldn't have needed all the extra information. They've given you the rate - 7 per hour - so it would be a simple equation: 45 x 7. Even I can work that out and I'm rubbish at maths! I think it's meant to be more complicated than that. They want you to work out how many parcels were wrapped in the final 45 hours in order to change the overall rate from 4 per hour to 7 per hour. I agree that it's poorly worded.

 

[jutfrank]

In my opinion, if they simply wanted the total number of gifts wrapped in the last 45 hours, they wouldn't have needed all the extra information.

Right. If the idea was supposed to be that 7 gifts per hour were wrapped in 45 hours, then there wouldn't be any calculation at all because the answer would be given in the question! Although it is imprecisely worded, it's obvious what calculation the puzzle writer wants you to do.

I'm confident that it isn't meant to be a trick question because it would be a rubbish trick. A trick question wouldn't be ambiguous. In any case, I think the wording itself leans more strongly toward the interpretation that we're thinking about the entire 60 hours.

 

[Glizdka]

First of all, I'd like to express my disappointment with how bad the girls are at their job. A measly seven per hour, really? The department store should seriously think about firing both of them and hiring this one as the sole employee in charge of wrapping gifts instead.

Second of all, how long are their shifts? For real, 60 hours seems like a tad too much. That employer's an exploitative fiend! I'm getting that the author wanted a neat, even 1:3 ratio here, but they could've easily said two hours and six hours. These numbers baffle me.

I understand that mathematicians are often detached from reality, especially when writing their math problem stories, but this one has clearly forgotten what labor laws are and how many hours there are in a day. This story's so bizarre that I'd have to forsake my rationale and just mindlessly plug in the numbers into my mind if I wanted to even begin processing the information. This should never be the case.

I would point out that gifts are countable and the author should've used "number of gifts", not "amount of gifts", but that's below me, so I'm only going to focus on the part that's caused all the confusion here.

"In a department store, with only one girl working on the gift-wrapping service, four gifts per hour were wrapped in the first 15 hours. With help from a colleague for the next 45 hours, the amount of gifts wrapped rose to seven per hour.
How many gifts were wrapped each hour in the last 45 hours only?"

If that's the exact instruction, then I think the part in bold is responsible for the confusion. If the author used "...the number of gifts was seven per hour" instead, then there would be no problem because you could just use "seven per hour" as your answer. That's not what they used, though.

If the author used "...the total number of gifts wrapped in the whole 60-hour period rose to seven per hour", then that would be precise and unequivocal, but that's not what they've gone for here.

When an average rises to something, there is some change and transformation going on. It means that the average of four per hour rose to seven per hour, so a continuation is implied, and the intended meaning is that we keep calculating the average from the very beginning, including when the gifts were being wrapped by only one of the girls. This is, however, just an implication. We're only trying to deduce what the author might have meant. This should never be the case. Math problem stories should be as clear as day; this one's as clear as mud.

I agree with you. This is poorly written.

 

[jutfrank]

When an average rises to something, there is some change and transformation going on. It means that the average of four per hour rose to seven per hour, so a continuation is implied

Yes, I agree that linguistically speaking, the heart of the matter lies in the interpretation of the verb rise and I agree that there is an implicit continuation.

However, you could still make a (weak) semantic argument that the continuation is temporal rather than numerical. I mean, you can calculate the average for the first period, and then calculate the average for the second period, and then still understand there being a continuation between the first and second periods. Obviously, if you're looking at the whole period globally, even if only comparing the different rates of the two periods, it still makes sense to understand that there's been a 'rise'. In other words, we could say that the average for period 1 was 4, and the average for period 2 was 7, and still say that a 'rise' from 4 to 7 had taken place.

(I hope that makes sense.)

 

[Glizdka]

(....) You could still make a (weak) semantic argument that the continuation is temporal rather than numerical. I mean, you can calculate the average for the first period, and then calculate the average for the second period, and then still understand there being a continuation between the first and second periods. Obviously, if you're looking at the whole period globally, even if only comparing the different rates of the two periods, it still makes sense to understand that there's been a 'rise'. In other words, we could say that the average for period 1 was 4, and the average for period 2 was 7, and still say that a 'rise' from 4 to 7 had taken place.

(I hope that makes sense.)

It does. And I agree, rose to could go either way, when isolated.

The fact the author has used "With help from a colleague for the next 45 hours..." right before it makes the reader more likely to interpret it that the seven per hour only describes the last 45 hours, not the whole 60-hour period. The passage's poorly written for that matter too.

 

[jutfrank]

The fact the author has used "With help from a colleague for the next 45 hours..." right before it makes the reader more likely to interpret it that the seven per hour only describes the last 45 hours, not the whole 60-hour period.

I agree with you and SoothingDave that for the next 45 hours plays a key role in the interpretation.

As the sentence stands, for the next 45 hours modifies help from a colleague. That is, the help lasted 45 hours. We can get that from the position of the comma. If you were to place the comma in a different position, the meaning would change, making for the next 45 hours modify the key clause the amount of gifts rose to seven per hour. Look:

With help from a colleague for the next 45 hours, the amount of gifts wrapped rose to seven per hour.

With help from a colleague, for the next 45 hours the amount of gifts wrapped rose to seven per hour.

 

[Borg]

With help from a colleague for the next 45 hours, the amount of gifts wrapped rose to seven per hour.

With help from a colleague, for the next 45 hours the amount of gifts wrapped rose to seven per hour.

Like most people, I really hate to admit that I'm wrong. But I see the difference in meaning between these two. The original question is written like the first sentence which places the emphasis for the rate away from the colleague's help. It's still a linguistic mess but if I had to pick two meanings for the rates in those two sentences, it's pretty clear which one goes with each sentence.

At one point, I tried reversing the sentence to see if I could understand it better. Unfortunately, I left off the colleague part and totally distorted it. If I had reversed the entire sentence around the comma, it would have made more sense.

The amount of gifts wrapped rose to seven per hour, with help from a colleague for the next 45 hours.

Instead, I did this:

The amount of gifts wrapped rose to seven per hour for the next 45 hours.

Thank you all for your responses and help!

 

[Glizdka]

The comma makes it very clear, but how sure can we be its correct position is intentional, not accidental?