Question

A small water pump would take 2 hours to fill an empty tank. A larger pump would take \small \frac{1}{2} hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?

Answer 1

Answer:

$FillingTime=0.4 [hours]$

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

$Ratio_{A} =\frac{Volume}{Time} =\frac{V}{2}[\frac{liters}{hours}]$

Pump B:

1/2 hour to fill the tank, so the ratio will be

$Ratio_{B} =\frac{Volume}{Time} =\frac{V}{1/2}=2V [\frac{liters}{hours}]$

So, to fill the tank with both pumps at the same time we sum both ratios to have the total filling ratio

$Ratio_{A+B} =\frac{V}{2} +2V=2.5V [\frac{liters}{hours}]$

Finally we have to calculate how much time takes to fill the tank of volume V with the new ratio:

$FillingTime=\frac{Volume [liters]}{FillingRatio[\frac{liters}{hours} ]} =\frac{V [liters]} {2.5V[\frac{liters}{hours} ]}=\frac{1}{2.5} [hours]=0.4 [hours]$