Question 615958
two pumps were required to pump the water out of a submerged area after a hurricane. 
Pump A, the large of the two pumps can pump the water out in 36 hours, whereas it would take pump B 180 hours.
Both pumps were working for the first 9 hours until pump A broke. 
How long did it take pump B to pump out the remaining water?
;
Let t = time to pump out the remain water
:
Let the completed job = 1, (all water pumped out)
:
{{{9/36}}} + {{{((t+9))/180}}} = 1
Reduce the fraction
{{{1/4}}} + {{{((t+9))/180}}} = 1
:
{{{((t+9))/180}}} = 1 - {{{1/4}}}
{{{((t+9))/180}}} = {{{3/4}}}
cross multiply
4(t+9) = 3 * 180
4t + 36 = 540
4t = 540 - 36
4t = 504
t = 504/4
t = 126 hrs to complete the job