how long does the whole operation tak?

Question

Pipe A fills a 5l tank at a rate of 15l per hour. Pipe B fills the same thank at a rate of 10 l/h. Pipe A runs alone for 100 minutes then the two of them together finish filling up the tank. How long does the whole operation take?

Answer 1

Nenalyn, maybe you meant the tank is 15 liters, and the rate in which Pipe A fills the tank is 5 l/hr. In this case, 100 minutes is 100/60 hr = 5/3 hr.

 

The volume in which Pipe A would fill the tank in 100 minutes is:

 

V1=5*5/3 = 25/3 liters

 

Subtract this from 15 liters in which is 45/3-25/3=20/3 liters.

 

Now this becomes a work problem in which the pipes are doing the work filling the tank. In order to set this problem as a work problem, you need to determine how long it would take for each pipe to fill the rest of the tank alone.

 

tA = how long it would take for Pipe A to fill the rest of the tank alone

tB = how long it would take for Pipe B to fill the rest of the tank alone

 

tA=20/3/5=4/3 hr

tB=20/3/10 = 2/3 hr

 

The equation for the time it would take for both pipes operating together to fill the rest of the tank is:

 

1/t=1/tA+1/tB. If you take the reciprocal and do some simplification the equation for t is:

 

t=tA*tB/(tA+tB) = 4/3*2/3/(4/3+2/3) = 8/9/(6/3)=8/9/2 = 4/9 hr 

 

Now add this to 5/3 hr in order to determine the total time for this operation.

 

T=5/3+4/9 = 15/9+4/9 = 19/9 hr = 19/9 hr*60min/hr ≅ 126.67 minutes