Answer:
[tex]FillingTime=0.4 [hours][/tex]
Both pumps take 0.4 hours to fill the tank, or 24 minutes.
Explanation:
First lets calculate the pumping ratio of each pump, assuming V as the volume of the tank:
Pump A:
2 hours to fill the tank, so the ratio will be
[tex]Ratio_{A} =\frac{Volume}{Time} =\frac{V}{2}[\frac{liters}{hours}][/tex]
Pump B:
1/2 hour to fill the tank, so the ratio will be
[tex]Ratio_{B} =\frac{Volume}{Time} =\frac{V}{1/2}=2V [\frac{liters}{hours}][/tex]
So, to fill the tank with both pumps at the same time we sum both ratios to have the total filling ratio
[tex]Ratio_{A+B} =\frac{V}{2} +2V=2.5V [\frac{liters}{hours}][/tex]
Finally we have to calculate how much time takes to fill the tank of volume V with the new ratio:
[tex]FillingTime=\frac{Volume [liters]}{FillingRatio[\frac{liters}{hours} ]} =\frac{V [liters]} {2.5V[\frac{liters}{hours} ]}=\frac{1}{2.5} [hours]=0.4 [hours][/tex]
