pls explain a question related to work and time

Question

two pipes A and B  fill a tank in 15 hours and 12 hours respectively. pipe B alone is kept open for 3/4 of the time and both the pipes are kept open for remaining time. in how many hours will the tank be full ?

Answer 1

Pipe B fills 1/12 of the tank per hour

Pipe A fills 1/15 of the tank per hour

 

Pipe B works alone for 3/4 of the hours =

1/12 per hour 3/4 of the time

Pipe A and B work together for 1/4 of the hours

(1/12 + 1/15) = 9/60 = 3/20 per hour for 1/4 of the time

 

 

(1/12)(3h/4) + (1/12 + 1/15)(h/4) = 1

h/16 + (9/60)(h/4) = 1

h/16 + (3/20)(h/4) = 1

h/16 + 3h/80 = 1

8h/80 = 1

h/10 = 1

h = 10 hours

 

Check:

Pipe B alone: (3/4)(10) = 15/2 hours ... 7.5 hours

(1/12)(15/2) = 5/8 full

 

Together: 2.5 hours .. 2 1/2 hours ... 5/2 hours

               (5/2)(3/20) = 3/8 full

 

5/8 + 3/8 = 8/8 = 1 .. tank is full