# One pump can fill a water tank in 40 minutes and another pump takes 30 minutes? How long will it take to fill the water tank if both pumps work together?

120/7=17.1428\ \text{min

#### Explanation:

Let $V$ be the total volume of tank then

Filling rate of first pump $= \frac{V}{40} \setminus$

Filling rate of second pump $= \frac{V}{30} \setminus$

If $t$ is the time taken by both the pumps to fill the same tank of volume $V$ then

$\setminus \textrm{V o l u m e f i l \le d b y \bot h p u m p \in t i m e t} = \setminus \textrm{V o l u m e o f \tan k}$

$\left(\frac{V}{40} + \frac{V}{30}\right) t = V$

$\left(\frac{1}{40} + \frac{1}{30}\right) t = 1$

$t = \setminus \frac{1}{\frac{1}{40} + \frac{1}{30}}$

$= \setminus \frac{120}{7}$

=17.1428\ \text{min

Hence, the total time taken by both pumps to fill the tank is 17.1428\ \text{min

Jul 27, 2018

$17.14$ minutes

#### Explanation:

To work this out we need to know the rate that the water is flowing with both pumps working.

Flow rate of pump1 $= \left(\text{1 Tank")/("40 min}\right)$

Flow rate of pump1 $= \left(\text{1 Tank")/("30 min}\right)$

So flow rate of pump 1 + pump 2

R_"both" = ("1 Tank")/("40 min") + ("1 Tank")/("30 min")

${R}_{\text{both"= ((30 +40) \ "Tank")/(30*40 \ "min") = (7)/(120) \ "Tank per min}}$

The reciprocal of rate is time so $T = \frac{120}{7} = \text{min per tank}$

$T = \text{17.143 min}$