There are two different inle

Question

There are two different inlet pipes that can be used to fill a 3000-gallon tank. Pipe A takes 6 hours longer than Pipe B to fill the tank. With both pipes open, it takes 3 hours to fill the tank. How long would it take Pipe B alone to fill the tank? Write an equation that could be used to model this problem. Let b represent the time (in hours) that it would take Pipe B alone to fill the tank.

Answer 1

This is a shared work problem. Usually they don't even give you the total volume or area, and as you'll see, it cancels in the end anyway.

 

Rate of filling by Pipe A =    3000       Rate of filling by Pipe B  =    3000          Rate of filling together  =    3000    

                                     (6 + b)                                                  b                                                        3

 

 

                   3000        +   3000      =     3000             (Notice how the 3000 cancels?)

                  (6 + b)              b                   3

 

          1      + 1   =    1         (Multiply all terms by (6 + b) )            
      (6 + b)     b         3        

 

          1    +  (6 + b)   =  6 + b      (Then, multiply all terms by b)

                        b               3

 

              b + (6 + b) = b(6 + b)        (Then, multiply all terms by 3)
                                       3

              3b + 3(6 + b) = b(6 + b)     (Multiply through, and simplify)

             3b   +  18  + 3b   = 6b   + b²

 

                6b   + 18    =   6b   +  b²

 

                             18 = b²

                                              

                             b  =   3√2     = 4.24 hours