Question 1208990
<pre>
<b><font color="blue">A 5-horsepower (hp) pump can empty a pool in 5 hours.</b></font>
So the larger pump's emptying rate is {{{matrix(1,2,1,pool)/matrix(1,2,5,hours))}}} or {{{matrix(1,2,expr(1/5),pool/hour)}}}

<b><font color="blue">A smaller, 2-hp pump empties the same pool in 8 hours.<b></font> 

So the smaller pump's emptying rate is {{{matrix(1,2,1,pool)/matrix(1,2,8,hours))}}} or {{{matrix(1,2,expr(1/8),pool/hour)}}}

<b><font color="blue">The pumps are used together to begin emptying this pool.</b></font>

Their rates add together so their combined rate is
{{{matrix(1,2,1/5+1/8,pool/hour)}}}{{{""=""}}}{{{matrix(1,2,8/40+5/40,pool/hour)}}}{{{""=""}}}{{{matrix(1,2,13/40,pool/hour)}}}

<b><font color="blue">After two hours,...     [the 2-hp pump breaks down.]</b></font>

So RATE x TIME = FRACTION of the pool EMPTIED

{{{matrix(1,2,13/40,pool/hour)}}}{{{""*""}}}{{{matrix(1,2,2,hours)}}}{{{""=""}}}{{{matrix(1,4,(13/40)*(2), of,the,pool)}}}{{{""=""}}}{{{matrix(1,4,13/20, of,the,pool)}}}

Since 13/20ths of the pool has been emptied, there remain 7/20th of the pool
to be emptied

<b><font color="blue">How long will it take the larger pump to empty the pool?</b></font>

Now the TIME is an unknown, so we use a letter, say t:  
Again, RATE x TIME = FRACTION of the pool EMPTIED, but now, we use only the rate
of the larger pump, 1/5, and only the remaining 7/20 of the pool to be emptied.
{{{matrix(1,2,1/5,pool/hour)}}}{{{""*""}}}{{{matrix(1,2,t,hours)}}}{{{""=""}}}{{{matrix(1,4,7/20, of,the,pool)}}}

So the equation is

{{{expr(1/5)*t}}}{{{""=""}}}{{{7/20}}}

Multiply both sides by 20

{{{4*t}}}{{{""=""}}}{{{7}}}

{{{t}}}{{{""=""}}}{{{7/4}}}

{{{t}}}{{{""=""}}}{{{1&3/4}}} hours

1 hour and 45 minutes.

Edwin</pre>