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?

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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"#