pipe a and pipe b fill the tank 15 & 20 min respectively how much time take if both fill the tank

Question

pipe A and pipe B fill the tank 15 and 20 minutes respectively how much time taken tank to fill if the both pipes are working

Answer 1

Pipe A fills 1/15 tank in 1 minute and pipe B fills 1/20 tank in 1 minute, so working together they fill 1/15+1/20=4/60+3/60=7/60 of a tank in 1 minute. So the time to fill the whole tank is 60/7 minutes=8 min 34.3 secs approx.

An easy way to check this is to assume the tank holds 60 gallons. Pipe A takes 15 mins to fill the tank, so it must be delivering 4 gallons a minute. Pipe B must be delivering 3 gallons a minute. Together they deliver 7 gallons a minute. So it takes 60/7 minutes for them to fill the tank working together.

Answer 2

let.........volume of the tank = V, rate of pipe 1 = R1 and rate of pipe 2 = R2

then........ R1 = V/15 and R2=V/20

⇒15R1 = 20R2 = V

thus... R1 = 4R2/3

but. .. R = R1 + R2

⇒R = 7R2/3................ = 7V/60

since..... R = V/t........... then 7V/60 = V/t

⇒t=60/7 min

It takes 8min and 34 sec{approximately}