Answer:
185 min
Step-by-step explanation:
Data
Pump a = Pa
Pump b = Pb
Full Tank = Ft
Tank = 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 Pb
if 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]
