Question 1177723
<br>
let x = # hours A takes alone to empty the pool
then x+2 = # hours B takes alone<br>
1/x = fraction of job A does in 1 hour
1(x+2) = fraction of job B does in 1 hour<br>
At 12pm when pump B broke down, A has been working 4 hours and B 2 hours.  The fraction of the job done at that time is<br>
{{{4(1/x)+2(1/(x+2))}}}<br>
That fraction of the job done at 12pm is 60% = 3/5. Solve that equation to find out how many hours A takes to empty the pool alone.<br>
{{{4(1/x)+2(1/(x+2)) = 3/5}}}<br>
Multiply through by the least common denominator {{{5(x)(x+2)}}}<br>
{{{20(x+2)+10(x)=3(x)(x+2)}}}
{{{30x+40 = 3x^2+6x}}}
{{{3x^2-24x-40 = 0}}}<br>
This does not factor; use the quadratic formula and of course use the positive root.<br>
{{{x = (24+sqrt(1056))/6}}} = 9.416 to 3 decimal places.<br>
2/5 of the pool remains to be emptied; the number of hours it will take A to finish is<br>
{{{9.416*0.4 = 3.7664}}}<br>
ANSWER: to a few decimal places, 3.7664 hours<br>