SOLUTION: it takes pump A two hours less time than Pump B to empty a swimming pool. Pump A is started at 8:00 am and pump B is started at 10:00. At 12:00 pm, 60% of the pool is empty when pu

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: it takes pump A two hours less time than Pump B to empty a swimming pool. Pump A is started at 8:00 am and pump B is started at 10:00. At 12:00 pm, 60% of the pool is empty when pu      Log On


   

Question 1117528: it takes pump A two hours less time than Pump B to empty a swimming pool. Pump A is started at 8:00 am and pump B is started at 10:00. At 12:00 pm, 60% of the pool is empty when pump B book down. How much time at 12 pm would it take pump A to empty the pool?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
t%5BA%5D=t%5BB%5D-2
So,
R%5BA%5D%2At%5BA%5D=100
R%5BA%5D=100%2Ft%5BA%5D
and
R%5BB%5D%2At%5BB%5D=100
R%5BB%5D=100%2Ft%5BB%5D
Substituting,
R%5BB%5D=100%2F%28t%5BA%5D%2B2%29
.
.
So at 12:00PM, Pump A has worked for 4 hours, Pump B for 2 hours to get 60% out.
R%5BA%5D%2A4%2BR%5BB%5D%2A2=%2860%2F100%29100
4R%5BA%5D%2B2R%5BB%5D=60
2R%5BA%5D%2BR%5BB%5D=30
Substituting,
2%28100%2Ft%5BA%5D%29%2B100%2F%28t%5BA%5D%2B2%29=30
20%2Ft%5BA%5D%2B10%2F%28t%5BA%5D%2B2%29=3
20%28t%5BA%5D%2B2%29%2B10t%5BA%5D=3t%5Ba%5D%28t%5Ba%5D%2B2%29
20t%5BA%5D%2B40%2B10t%5BA%5D=3t%5BA%5D%5E2%2B6t%5BA%5D
3t%5BA%5D%5E2-24t%5BA%5D-40=0
t%5BA%5D%5E2-8t%5BA%5D-40%2F3=0
t%5BA%5D%5E2-8t%5BA%5D%2B16-40%2F3=16
%28t%5BA%5D-4%29%5E2=48%2F3%2B40%2F3
%28t%5BA%5D-4%29%5E2=88%2F3
t%5BA%5D-4=0+%2B-+sqrt%2888%2F3%29
t%5BA%5D=4+%2B-+sqrt%2888%2F3%29
Only positive solutions allowed,
t%5BA%5D=4%2Bsqrt%2888%2F3%29
So then we need to find the new time, T, it takes Pump A to empty the remaining 40% of the pool.
R%5BA%5D%2AT=%2840%2F100%29100
R%5BA%5D%2AT=40
T=40%2FR%5BA%5D
T=40%28t%5BA%5D%2F100%29
T=%282%2F5%29%284%2Bsqrt%2888%2F3%29%29
T=%282%2F5%29%284%2B%282%2F3%29sqrt%2866%29%29
highlight%28T=8%2F5%2B%284%2F15%29sqrt%2866%29%29hrs