A machine can process 300 parts in 20 min. How many parts can be processed in 45 min?

Question

How would you solve this particular word problem?

Answer 1

We assume that the machine in the problem has a constant production rate (parts per minute):

     parts per minute  =  parts per minute = parts per minute

This means that we can set up a proportion as:

     (300 parts)/(20 min) = (x parts)/(45 min)

 

We could also consider the constant duration (time for each part):

     (20 min)/(300 parts) = (45 min)/(x parts)

 

That is, the proportion was simply inverted.

 
We also could observe that parts and minutes are proportional:

     (20 min)/(45 min) = (300 parts)/(x parts)

And, inverting that:

     (45 min)/(20 min) = (x parts)/(300 parts)

 

What is important is, that when we cross-multiply any of these, we get:

     (300 parts)*(45 min) = (x parts)*(20 min)

(note: we can work that equation backward to get any of the previous proportions !)

 

Now, the only thing to watch out for is mixing units.  For example,

    (300 parts)(x parts) ≠(20 min)(45 min)

    (parts^2 does not equal min^2)

 

So, be sure to include units and you’re almost there.

 

Once the ratio or equation is set up, the math should be easy.

Answer 2

To keep it simple, you need to figure out how many parts can be produced in just one minute.  You figure this out by dividing 300 with 20, which = 15.  Next, multiply 15 and 45 to figure out how many parts can be produced in 45 minutes.  The writen equation looks like this:

 

300 parts              X parts 

_________    =        __________

 

20 minutes         45 minutes 

 

Now crisis cross multiply which should look like 

 

300 * 45 = x * 20

 

13,500 = 20x.

 

Get your #'s on one side of the = sign and your letters on the other by dividing.

 

13,500 ÷20 = x

 

X = 675

Answer 3

I would use proportions on something like this. 

Set the #s up as  (min of 1st)/(how many parts in those minutes) = (min of 2nd)/x, where x is unknown. Cross multiply next.