Question 162045
<pre><font size = 4 color = "indigo"><b>
If a pipe can fill a tank in x hours, what fractional 
part of the tank will be filled in one hour?

Let's look at a bunch of particular cases when we have a
number instead of the letter "x":

Case 1: 
If a pipe can fill a tank in {{{1}}} hour, what fractional 
part of the tank will be filled in one hour?  Answer: {{{1/1}}}th of it. 

[That's 1, or 100%, or all of it]

Case 2:
If a pipe can fill a tank in {{{2}}} hours, what fractional 
part of the tank will be filled in one hour?  Answer: {{{1/2}}} of it.

Case 3: 
If a pipe can fill a tank in {{{3}}} hours, what fractional 
part of the tank will be filled in one hour?  Answer: {{{1/3}}}rd of it.

Case 4: 
If a pipe can fill a tank in {{{4}}} hours, what fractional 
part of the tank will be filled in one hour?  Answer: {{{1/4}}}th of it.

Case 5: 
If a pipe can fill a tank in {{{5}}} hours, what fractional 
part of the tank will be filled in one hour?  Answer: {{{1/5}}}th of it.

Case 6: 
If a pipe can fill a tank in {{{6}}} hours, what fractional 
part of the tank will be filled in one hour?  Answer: {{{1/6}}}th of it.
  
Case 7: 
If a pipe can fill a tank in {{{7}}} hours, what fractional
part of the tank will be filled in one hour?  Answer: {{{1/7}}}th of it.

...

Now that list can go on forever and ever.  But look at what 
is always true in every case above:

If a pipe can fill a tank in a certain number of hours, what 
fractional part of the tank will be filled in one hour?  

The answer is always {{{1/("that_certain_number")}}}ths of it.

So if we replace the words "that certain number" by the letter 
"x" you could say this about every one of those:

Case x: 
If a pipe can fill a tank in {{{x}}} hours, what fractional part 
of the tank will be filled in one hour?  Answer: {{{1/x}}}ths of it.

So the answer is {{{1/x}}}.

Edwin</pre>