Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute).
Accepted Solution
A:
Answer:185 minStep-by-step explanation:DataPump a = PaPump b = PbFull Tank = FtTank = T we have that Pa fills T in 5 hours and Pb fills the same tank in 8 hours, we must find that T capacity is filled in one hour by Pa and Pbif Pa fills T in 5h, in 1h what capacity is filled, [tex]Pa=\frac{h*Ft}{5h}=\frac{Ft}{5}[/tex] ; if Pb fills T in 8h, in 1h what capacity is filled, [tex]Pb=\frac{h*Ft}{8h}=\frac{Ft}{8}[/tex], and now we must find: How long will Pa and Pa be used together to fill T. [tex]Pa+Pb = \frac{Ft}{5}+\frac{Ft}{8}=\frac{13Ft}{40}[/tex]; The capacity of T = 40/40, so if Pa+Pa in 1h fill [tex]\frac{13Ft}{40}[/tex] then to fill 40/40 in h=? [tex]\frac{1h*\frac{40}{40}Ft }{\frac{13Ft}{40}}=\frac{\frac{40Ft.h}{40}}{\frac{13Ft}{40}}=\frac{40h}{13}[/tex], but h must be in min so[tex]\frac{40h}{13}*\frac{60min}{h}=185 min[/tex]