Need help pls

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Devaraja

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How would I solve this? I need steps pls.
25 students work on project 30 days. After 8 days 5 students quit. how much more days will they now need to finish project
 
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The first thing to do, though, is to figure out what it means. It is not very clear. It says that they work for 30 days, so don't they just have 22 days left until the deadline, and those who remain just have to work harder?

Unless you didn't quote the problem exactly (as we ask you to do), you are probably expected to guess that the job requires exactly as much time (in "person-days") as those 25 students would have put in over 30 days, and are allowed to take longer with fewer people.

But the method for solving this depends on what you know. I would use the person-day idea; but there are several ways you might use proportions or equations. This is why we want to see some work, or at least a description of what you have been taught, or an example you have been given. There is not just one list of steps to follow; in fact, problem-solving in general does not involve known steps. It involves thinking about how to use the tools you have.
 
Devaraja said:
How would I solve this? I need steps pls.
25 students work on project 30 days. After 8 days 5 students quit. how much more days will they now need to finish project
Click to expand...
When all 25 are working - how much work gets done by one (1) student per day?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
Hi, and thanks for your answers. First an explanation 25 students worked for 8 days after that 5 students left and their deadline is 30 days. Now I need to know how much more then 30 days remaining students will need to finish project?
Btw sorry I'm asking for steps, I'm a mom and this is for my daughter school assignement and we just can't figure out how to get steps done.
We know that solution is 5.5 days because in book answer says 27.5+8= 35.5 so day need extra 5.5 days, but I don't know how they come up with 27.5?
 
Devaraja said:
Hi, and thanks for your answers. First an explanation 25 students worked for 8 days after that 5 students left and their deadline is 30 days. Now I need to know how much more then 30 days remaining students will need to finish project?
Btw sorry I'm asking for steps, I'm a mom and this is for my daughter school assignement and we just can't figure out how to get steps done.
We know that solution is 5.5 days because in book answer says 27.5+8= 35.5 so day need extra 5.5 days, but I don't know how they come up with 27.5?
Click to expand...
You need to answer the question I had asked:

When all 25 are working - how much work (fraction of total work) gets done by one (1) student per day?
 
Devaraja said:
Hi, and thanks for your answers. First an explanation 25 students worked for 8 days after that 5 students left and their deadline is 30 days. Now I need to know how much more then 30 days remaining students will need to finish project?
Btw sorry I'm asking for steps, I'm a mom and this is for my daughter school assignement and we just can't figure out how to get steps done.
We know that solution is 5.5 days because in book answer says 27.5+8= 35.5 so day need extra 5.5 days, but I don't know how they come up with 27.5?
Click to expand...
First, 30 days is not really the deadline (which would mean they couldn't work after that); I said that to get you to think about what it is intended to mean. The idea is that if all 25 worked for 30 days, they would get the entire job done, but now they have fewer, so it will take longer to get the same amount of work done at the same rate (not working harder to beat the deadline).

Subhotosh's question is the next step after understanding what it means: how much of the job does one student do in one day? There are a couple ways to think of this, so we want to leave this for you to decide based on how the book teaches it, which we can't see.

Once you find that, you can determine how much of the job was done in the first 8 days, and then how much remains to be done after that. (These will all be fractions, or perhaps percents.)

Then you will find how long it will take the remaining 20 students to get that much work done, at the rate you determined; the answer presumably will be 27.5, which you'll add to the 8 days already spent.

It may help if you can show us what topic has been taught, and perhaps an example, so we can see better how the book explains things, and therefore what your daughter can be expected to understand. When I tutor face-to-face, I often ask to look at the book for this reason; here, I have to ask for whatever you can tell me.
 
Devaraja said:
I guess that would be 0.83
Click to expand...
If your answer to the question:

how much work (fraction of total work) gets done by one (1) student per day? = 0.83 ............... it is incorrect.

I would calculate as follows:

25 students can work for 30 days and finish full project 1

25 students can work for 1 day and finish 1/30 part of the project

1 student can work for 1 day and finish [1/(30*25)=1/750=] 0.001333 part of the project

However, I would keep the fractional representation (1/750)

continue.....

How did you calculate it? Please show your work.
 
Last edited by a moderator:
Subhotosh Khan said:
If your answer to the question:

how much work (fraction of total work) gets done by one (1) student per day? = 0.83 ............... it is incorrect.

How did you calculate it? Please show your work.
Click to expand...
I calculate it like this. 25/30=0.83
Dr.Peterson said:
First, 30 days is not really the deadline (which would mean they couldn't work after that); I said that to get you to think about what it is intended to mean. The idea is that if all 25 worked for 30 days, they would get the entire job done, but now they have fewer, so it will take longer to get the same amount of work done at the same rate (not working harder to beat the deadline).

Subhotosh's question is the next step after understanding what it means: how much of the job does one student do in one day? There are a couple ways to think of this, so we want to leave this for you to decide based on how the book teaches it, which we can't see.

Once you find that, you can determine how much of the job was done in the first 8 days, and then how much remains to be done after that. (These will all be fractions, or perhaps percents.)

Then you will find how long it will take the remaining 20 students to get that much work done, at the rate you determined; the answer presumably will be 27.5, which you'll add to the 8 days already spent.

It may help if you can show us what topic has been taught, and perhaps an example, so we can see better how the book explains things, and therefore what your daughter can be expected to understand. When I tutor face-to-face, I often ask to look at the book for this reason; here, I have to ask for whatever you can tell me.
Click to expand...
Thanks for your help I think I got it:
30:25=1.2
1.2:25=0.05
0.05*8=0.4
1 student does 0.4 work per day.
25*0.4=10 per day
10*30=300 of the job needs to be done.
10*8=80 of the job has been done.
300-80=220 job left to do.
20*0.4=8
220/8=27.5
27.5+8=35.5
35.5-30= 5.5
Is this to advanced for 12y old child to figure out on it's own?
 
I'll insert comments in your answer:
Devaraja said:
I calculate it like this. 25/30=0.83 <--- This would be measured in units of students per day, which doesn't make sense for this problem

Thanks for your help I think I got it:
30:25=1.2 <--- This would be days per student, which again is inappropriate
1.2:25=0.05 <--- This would be days per student per student; and it's rounded, so you've lost accuracy
0.05*8=0.4 <--- This would be in days times days per student per student
1 student does 0.4 work per day. <--- No, this is not true. See what Subhotosh did to find that it's 1/750 of the job per student per day.
25*0.4=10 per day <--- If this were true, then the 25 students would do the job 10 times over each day!
10*30=300 of the job needs to be done. <--- They'd do 300 of the job in the 30 days???
10*8=80 of the job has been done.
300-80=220 job left to do. <--- If your numbers made sense, these three lines would be right
20*0.4=8 <--- This would mean the 20 remaining students do 8 jobs per day
220/8=27.5 <-- The fact that you got this correct number implies that somehow your wrong numbers were in the right proportion
27.5+8=35.5
35.5-30= 5.5
Is this to advanced for 12y old child to figure out on it's own?
Click to expand...
I would still like to see what she has been taught, since presumably that should prepare her to do this thinking.

Here is what I would do, following my advice; you'll observe that one key is to always state what each number means, as I did above.

Repeating Subhotosh's work, and continuing:​
​
25 students do the one job in 30 days​
25 students do 1/30 of the job in 1 day​
1 student does (1/30)/25 = 1/750 of the job in 1 day. So rather than your 0.4 job per student per day, it's 0.00133... .​
​
Now, in 8 days, 25 students do 8*25*1/750 = 4/15 of the job.​
The remaining amount of work is 1 = 4/15 = 11/15 of the job.​
20 students can do 20*1/750 = 2/75 of the job per day.​
To do 11/15 of the job at a rate of 2/75 job per day will take (11/15)/(2/75) = 11/15*75/2 = 55/2 = 27.5 days​

And you know the rest.

After your incorrect rate of 0.4 (which is 300 times as large as it should be), all of the things you did were correct, just using the wrong rate. Your 220 jobs is 300 times as much as it should be, and your 8 jobs per day for the 20 students is also 300 times too large, so their ratio gave you the correct number. (If you hadn't rounded, it would have been 288 times too large.)

Now, observing that it didn't matter that you got a wildly wrong rate, I suspect that the rate doesn't even matter!

I'm going to try doing this the way I initially thought I'd do it, and see if it's easier:

In 8 days, they did 8/30 = 4/15 of the work, so 1 - 4/15 = 11/15 of the work remains. The 20 students will work at 20/25 = 4/5 of the rate of the whole group, so it will take 5/4 as long as it would have. So work that would have taken 22 days instead takes 5/4 * 22 = 27.5 days. And I didn't even have to use the first sentence of this paragraph!​

That's all we really need: a proportion. And that is probably what your daughter has been taught. On the other hand, it is obviously easy to find a harder way to do it.
 
Here is how I would do this problem so you could help explain it to your daughter.

25 students working on the project will take 30 days. So the job requires 25*30 students-days, ie 750 student days to get the job done..

After 8 days with 25 students they completed 8*25 = 200 student days. So 750 - 200 = 550 student-days left. Now only 20 students are working. You need to solve 20students * x days = 550 student-days. Dividing both sides by 20 student-days gives us x = 550/20 = 27.5

They already worked for 8 days and need 27.5 more days to complete the job. That will be a total of 35.5 days which is 5.5 more days than originally planned for.
 
Thank you everyone for explanation, Il try to teach her that way. It was hard because in book there is no example for that kind of task. Also the lesson they learning is inverse proportions. Thank you all again.
 
Devaraja said:
Thank you everyone for explanation, Il try to teach her that way. It was hard because in book there is no example for that kind of task. Also the lesson they learning is inverse proportions. Thank you all again.
Click to expand...
Then my final method is almost certainly what they expect, as I used an inverse proportion. It's unfortunate that it's fairly well hidden, so that we saw other ways first, but now we know.
 
Just a little update. Nobody in my daughter class has done that task so because teacher didn't teach them how to do it but still she gave them that for homework. Anyway when she saw they didn't know how to do it she showed them even easier way, like this:
30-8=22
22*25/20=27.5
 
Devaraja said:
Just a little update. Nobody in my daughter class has done that task so because teacher didn't teach them how to do it but still she gave them that for homework. Anyway when she saw they didn't know how to do it she showed them even easier way, like this:
30-8=22
22*25/20=27.5
Click to expand...

That is the same as my final method that I said was almost certainly what was expected:
Dr.Peterson said:
The 20 students will work at 20/25 = 4/5 of the rate of the whole group, so it will take 5/4 as long as it would have. So work that would have taken 22 days instead takes 5/4 * 22 = 27.5 days. ​

That's all we really need: a proportion. And that is probably what your daughter has been taught. On the other hand, it is obviously easy to find a harder way to do it.
Click to expand...
 
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