I was always so bad at these when I was in school. I came across this problem in my daughter’s math textbook (6th grade), how stupid I feel for not knowing the formula to figure it out.
If 5 students can dig a 5 meter ditch in 5 hours, how many students will it take to dig a 100 meter ditch in 100 hours?
I’d like to be able to show her how to work the problem so she can figure it out for herself. I might learn something as well.
Can anyone help?
Oh yeeps.These crop up all the time 
Normally it’s men running baths or digging 10 foot trenches
It’s not the obvious AFAIK…so I wouldnt go for 100…I’ll check for you on the Net.
Do I get a reward for getting it right…
I’ve googled til I can’t google no more. I can’t figure it out. My guess would be 1 but, I need to be sure with some type of formula.
six_personalities I will reward you with one of these and a huge thank you!
Forget the number of students for the time being. look at the rate of growth of the ditch
5 meters in 5 hours = 1 meter per hour
100 meters in 100 hours = 1 meter per hour
Therefore those same 5 students can dig the 100 meter ditch in 100 hours
I think its more a ‘thinking things through’ sort of problem.
If five students dig a five metre ditch in five hours, then it will take one student five times five hours to dig a five metre ditch - 25 hours. Therefore, to dig a 100 metre ditch, it would take one student 20 times 25 hours (since five times 20 is 100) - 500 hours. But you only have 100 hours, therefore, you need 5 students to get 500 hours of work done in 100 hours.
But don’t forget to figure in time for meals, sleeping and potty breaks. 100 hours is a long time to work digging a ditch.
Thank you so much. I was making it too complicated.
You get the
Ask your daughter this: how many meters per hour can 5 students dig a trench?
5 students can dig a 5 meter trench in 5 hours.
So, 5 students can dig a 1 meter trench in 1 hour.
So, 5 students can dig at the rate of 1 meter per hour.
That’s the way to look at a problem like that.
If you really want to break it down mathematically, you can calculate how fast each student digs.
If, 5 can dig 5 meters in 5 hours. So 5 can dig 1 meter in 1 hour. So 1 can dig 1/5 meter per hour. That means it would take 1 student 500 hundred hours to dig a 100 meter trench. So, it would take 5 students 100 hours to dig a 100 meter trench.
Thanks! I’ll add it to the collection…
Oh who am i kidding - i’ll start the collection
Is that all?I wanted cash 
Collection of what? It’s the :). Singular definite article.
And economies of scale. What the problem didn’t tell you is that the students really dig at five meters per hour, but the first four hours were spent requisitioning the supplies. A 100-meter ditch will only take 24 hours. 20 if they hold onto the supplies from this project.
You also must consider that the 5 students have already dug 5 meters of ditch. So they only have to dig another 95 meters.
And one other thing : students don’t dig ditches. Drop-outs dig ditches.
This is the same as the classic “if a chicken and a half can lay an egg and a half in a day and a half, how many eggs can six chickens lay in six days?”
collection of 's
every collection starts with 1 and that’s the 1st one i’ve been awarded!
Another approach is to write an equation for the problem.
Let w = amount of work in meters
s = number of students
t = time in hours
r = rate of work for one student in meters/hour
So w = str
For the first problem, w = 5, s = 5, t = 5, r = unknown.
5 = 55r
5 = 25r
r = 5/25 = 1/5
For the second problem, w = 100, s = unknown, t = 100, r = 1/5
100 = s1001/5
100 = s*20
s = 100/20 = 5
Thanks for all the responses everyone. Ya gotta love a place where you can ask a 6th grade math question, even though you’ve been out of school for 20 years, and no one makes fun of you.
Honey
Nelson Muntz mode on Har-har
Here’s how I would do it, if I had to solve it systematically:
5 meters in 5 hours is a rate of 1 meter per hour. That’s for 5 students, so each student can do 1/5 meter per hour. Now you need to dig 100 meters in 100 hours, so you need enough manpower to get a rate of 1 meter per hour. The number of students you need is (required rate)/(rate per student) = 1/(1/5)=5 students.
This is basically what mks57 said, but I think it looks less scary without variables. 
And the magical faerie who will come and turn the shovels into pixies who can use their hands to dig and dig and dig and dig without pay checks or potty breaks.
Of course, since the book didn’t mention that sort of stuff, it probably can be assumed that the goal is to learn how to utilize a particular type of reasoning, mathematics perhaps, rather than avoid learning it by making up all sorts of fun little stories.