It takes 30 minutes to empty a half full tank by draining it at constant rate. It is decided to simultaneously pump water into the half full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes?

• @ 1/15 per minute
  
  It will completely drain full tank in 2*30=60 minutes. So rate of draining=1/60 per minute
  If only pumping takes 'x' minutes to fill empty tank, then pumping rate=1/x per minute
  So to completely fill the half filled tank in 10 minutes, (1/2) + 10*[(1/x)-(1/60)]=1, 1/x=1/15
• 8 years agoHelpfull: Yes(18) No(3)
• 1/x- 1/30= 1/10. solve for x. we get 1/15.
• 7 years agoHelpfull: Yes(9) No(4)
• answer will be 4 times the draining rate.
  
  the equation to use is RT = Q
  Q is equal to 1/2 the tank.
  T is equal to 30 minutes
  R is derived from the equation as follows:
  RT = Q
  R*30 = 1/2
  R = 1/60
  the tank is being drained at the rate of 1/60 of the tank per minute.
  at that rate, the remaining 1/2 of the tank will be drained in 30 minutes.
  
  the rate of filling and the rate of draining are opposing forces so you need to subtract one from the other to get the rate of filling.
  
  you want to fill 1/2 the tank while at the same time you are draining the tank.
  the combined formula would be as follows:
  (RF - RD) * 10 = 1/2
  you know RD is 1/60 because we just solved for that.
  your formula becomes:
  (RF - 1/60) * 10 = 1/2
  simplify this to get:
  10*RF - 10/60 = 1/2
  add 10/60 to both sides of this equation to get:
  10*RF = 1/2 + 10/60 which becomes:
  10*RF = 30/60 + 10/60 which becomes:
  10*RF = 40/60.
  divide both sides of this equation by 10 to get:
  RF = 4/60.
  
  4/60 is 4 times 1/60.
• 7 years agoHelpfull: Yes(2) No(4)
• 1/40
  1/10=x-1/30
  x=4/30
  x is rate at which water has to be pumped
  it is given that tank is half filled
  only half tank has to be pumped
  
• 7 years agoHelpfull: Yes(0) No(3)