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?

Question

9682 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-27T12:59:53

$120/7=17.1428\ \text{min$

Let $V$ be the total volume of tank then

Filling rate of first pump $=V/40\$

Filling rate of second pump $=V/30\$

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

$\text{Volume filled by both pump in time t}=\text{Volume of tank}$

$(V/40+V/30)t=V$

$(1/40+1/30)t=1$

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

$=\frac{120}{7}$

$=17.1428\ \text{min$

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

Answer 2 · 2018-07-27T13:31:40

$17.14$ minutes

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

Flow rate of pump1 $= ("1 Tank")/("40 min")$

Flow rate of pump1 $= ("1 Tank")/("30 min")$

So flow rate of pump 1 + pump 2

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

$R_"both"= ((30 +40) \ "Tank")/(30*40 \ "min") = (7)/(120) \ "Tank per min"$

The reciprocal of rate is time so $T = 120/7 = "min per tank"$

$T= "17.143 min"$