dividing a load of work correctly

[artiscon]

Hello. My first post. Seems such a simple question but I can not work it out.

Two teachers are sharing a classroom of 15 students. Person A teaches 75% of normal working hours. Person B teaches 50% of normal working hours.
When it comes to marking students, how many should person A mark and how many person B?

thank you

Tony

 

[stapel]

Two teachers are sharing a classroom of 15 students. Person A teaches 75% of normal working hours. Person B teaches 50% of normal working hours.

Does this mean that they overlap for at least 25% of the time?

When it comes to marking students, how many should person A mark and how many person B?

I don't know. What algorithm are you supposed to apply? What are the rules?

 

[NerdBoy628]

I think I might know it:

A teaches 75%, and B teaches 50%, making a total of 125%.
A teaches 75/125 = 3/5 of the time.
B teaches 50/125 = 2/5 of the time.
3/5 of the 15 students is 9, so person A should mark 9 students.
2/5 of the 15 students is 6, so person B should mark 6 students.

 

[khansaheb]

Hello. My first post. Seems such a simple question but I can not work it out.

Two teachers are sharing a classroom of 15 students. Person A teaches 75% of normal working hours. Person B teaches 50% of normal working hours.
When it comes to marking students, how many should person A mark and how many person B?

thank you

Tony

Is this a problem that was assigned to you in an instructional class or a practical problem?

The problem statement is vague - mainly because (75%+50%) > 100%. Are you paraphrasing the problem?

If possible, report the exact problem as it was given to you.

 

[khansaheb]

I think I might know it:

A teaches 75%, and B teaches 50%, making a total of 125%.
A teaches 75/125 = 3/5 of the time.
B teaches 50/125 = 2/5 of the time.
3/5 of the 15 students is 9, so person A should mark 9 students.
2/5 of the 15 students is 6, so person B should mark 6 students.

Did you realize that you "could have" made several important & implicit assumptions - which "could be" as follows:

1. 'A' teaches subject S₁ to 15 students and 'B' teaches subject S₂ to 15 students
   - In that case if 'A' cannot mark S₂ and 'B' cannot mark S₁
   - then both 'A' & 'B' will have to grade 15 papers each
2. 'A' teaches subject S₃ to 15 students and 'B' teaches subject S₃ to 15 students
   - In that case if 'A' cannot mark S₂ and 'B' cannot mark S₁
   - then then your 'scheme' will be sort of fair.

Which assumption (1 or 2 or something else) did you make?
What other "possible" assumption/s did you make - for your calculations?

 

[eipi45]

This is a ratio question.
The ratio of work is A:B = 75:50

So to answer the question , divide the 15 students in the ratio 75:50

 

[Dr.Peterson]

This is a ratio question.
The ratio of work is A:B = 75:50

So to answer the question , divide the 15 students in the ratio 75:50

That's probably the intent, as a school problem. And it's convenient that the numbers work out neatly (unlike the real world), eliminating the need to think about how to round.

But in the real world, you could never make such a simple assumption. I am very unhappy with problems where the "obvious" thing to do is to assume proportionality without good reason.

Two teachers are sharing a classroom of 15 students. Person A teaches 75% of normal working hours. Person B teaches 50% of normal working hours.
When it comes to marking students, how many should person A mark and how many person B?

We know nothing of the details of the work situation (which seems to be quite odd), and how they are intended to share the job.

One possibility that occurs to me: Perhaps the 25% overlap is when they are teaching different groups within the class (perhaps 5 students with special needs taught by A, while B teaches the rest a subject the former don't need).

But then, another question is what it means to "mark students". If it means doing all the grading for a subset of the class, then A might be the one to handle his 5 students, while B would handle her 10, regardless of time spent.

There are so many possible scenarios, there's no way to answer without knowing the details. And mathematics should never teach students to ignore details!

 

[The Highlander]

This is a ratio question.
The ratio of work is A:B = 75:50

So to answer the question , divide the 15 students in the ratio 75:50

It may not be as simple as that.

Along with the possibilities raised at Posts #4 & #7, one might also have to consider the further possibility that both teachers ought to take an equal share of the marking (as a potential result of the anomaly implied by the given percentages of "normal working hours").

If the class were being taught by one teacher then one would expect the class to spend all its time with that teacher within 100% of that teacher's normal working hours.

However these teachers are working 125% of normal working hours so one potential conclusion is that 25% of normal working hours are not spent with that class; meaning one (or both) of these teachers spends some time not teaching this class!

This would likely be further complicated by the fact that it unusual for any teacher to spend 100% of their normal working hours with a single class!

Much more information is required to make any sense of the problem.

 

[eipi45]

But in the real world, you could never make such a simple assumption

It may not be as simple as that.

In exam questions there are conventional simplifications.
Circles are perfectly circular, smooth inclined planes are perfectly smooth, random selections are uniform unless otherwise stated.

This question is very straightforward indeed; two teachers work at an institution, one at 0.75 of FT and one at 0.5 of FT

A class they both happen to teach (whether simultaneously, remotely or howsoever) has 15 students and their work has to be marked , and the two teachers are expected to do the marking between them in a way that reflects their remuneration.