SOLUTION: A large and small inlet pipe work together to fill a storage tank. The larger pipe requires 8 hrs working alone to fill the tank. After both pipes have been operating for 3 hrs, th

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A large and small inlet pipe work together to fill a storage tank. The larger pipe requires 8 hrs working alone to fill the tank. After both pipes have been operating for 3 hrs, th      Log On


   

Question 662322: A large and small inlet pipe work together to fill a storage tank. The larger pipe requires 8 hrs working alone to fill the tank. After both pipes have been operating for 3 hrs, the larger pipe is turned off. The small pipe requires 10 more hours to fill the storage tank. How long would it take the smaller pipe working alone to fill the tank?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Large pipe's filling rate = %281_tank%29%2F%288_hr%29 = 1%2F8tank%2Fhr

Small pipe's filling rate = %281_tank%29%2F%28x_hr%29 = 1%2Fxtank%2Fhr

Filling rate working together = %281%2F8%2B1%2Fx%29tank%2Fhr

Part of tank filled in first 3 hours = 3·%281%2F8%2B1%2Fx%29
Part of tank filled in next 10 hours = 10·%281%2Fx%29

      The equation comes from

              +  = %28matrix%283%2C1%2C%0D%0A%0D%0A1%2Ctank%2Cfilled%29%29

 
            3·%281%2F8%2B1%2Fx%29 + 10·%281%2Fx%29 = 1 

Solve that and get 20.8 hours. 

Edwin