Question

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?

Answer 1

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

Explanation:

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

`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 `= ("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"`