Question 98661


       A hose can fill a swimming pool in 6 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool? 

          Time taken by horse A to fill the pool = 6 hrs

          Time taken by horse B to fill the pool = y hrs

          Time taken by both together to fill the pool = x hrs

                       therefore y = x+3........(1)

         qn'ty filled by horse A in 1 hr = 1/6

         qn'ty filled by horse B in 1 hr = 1/y
         qn'ty filled by both in 1 hr = 1/x

           therefore 1/x = 1/6+1/y........(2)

        substituting for y in eq'n (2) we get

                    1/x = 1/6+1/(x+3)

                   1/x = x+3+6/6(x+3)

                   1/x = x+9/6(x+3)

                  6(x+3) = x(x+9)

                   6x+18 = x^2+9x

                    x^2+9x-6x-18 = 0
                    x^2+3x-18 = 0

                     x^2+6x-3x-18 = 0

                     x(x+6)-3(x+6)= 0

                       (x+6)(x-3)= 0

             substituting for x in eq'n (1)   we get y = x+3

                             x-3 = 0 or x = 3  therefore y = 3+3 = 6

       Horse B would take 6 hrs to fil the pool