no idea: It takes 8 machines to do a job in 6 days. How many

[jdgamble]

It takes 8 machines to do a job in 6 days. How many machines would it take to do the job in 1 day and a half?

I first thought this:

8/6 = x/1.5

this results in x being 2, which is not right. It CAN'T take less machines to do a job in less time right? So how do you solve this problem? I know the answer is 96, but I don't know where it came from and how to solve future related problems.

Help please.

Thanks,

 

[TchrWill]

Re: no idea what kind of problem

It takes 8 machines to do a job in 6 days. How many machines would it take to do the job in 1 day and a half?

I first thought this: 8/6 = x/1.5

this results in x being 2, which is not right....

..............Machines...Days
If it takes.....8...........6
It will take...48..........1
It will take...32........1.5

 

[Mrspi]

Re: no idea what kind of problem

It takes 8 machines to do a job in 6 days. How many machines would it take to do the job in 1 day and a half?

I first thought this:

8/6 = x/1.5

this results in x being 2, which is not right. It CAN'T take less machines to do a job in less time right? So how do you solve this problem? I know the answer is 96, but I don't know where it came from and how to solve future related problems.

Help please.

Thanks,

As you've noted, it should take MORE machines to do the job in LESS time. This suggests that there is an inverse relationship between the number of machines used and the time it takes to do the job. The number of days varies INVERSELY as the number of machines used.

The basic formula for inverse variation is

xy = k

Let x = number of machines
Let y = number of days

We know it takes 8 machines 6 days to complete the job, so

8*6 = k
48 = k

And the formula for this particular inverse variation situation is
xy = 48

Ok...now, what if the number of days is 1.5? Substitute 1.5 for y:

x*1.5 = 48
1.5x = 48

Solve for x......and no, the correct answer is NOT 96.

I hope this helps you.

 

[jdgamble]

hmmm

Inverse variation:

xy = k

I'm trying to remember this stuff. So what does k equal? If in this case x = number of days and y = machines, what does k equal? I'm a little lost.

 

[skeeter]

Re: hmmm

Inverse variation:

xy = k

I'm trying to remember this stuff. So what does k equal? If in this case x = number of days and y = machines, what does k equal? I'm a little lost.

xy = k ... k is a constant of proportionality (it never changes)

(8 machines)(6days) = k
k = 48

so ...

(x machines)(1.5 days) = 48

x = 48/1.5 = 32 machines

 

[jdgamble]

Thanks, that helps!