Question

working alone, john takes two more hours to clean thehouse than jane does. if they work together, john andjane can clean the house in 2 hours 24 minutes. how longdoes it take john to clean the house if he is workingalone?

Answer 1

Jhon will take 6 hours to compete the same work

Men and work :

             This question is based on the concept of men and work

given,

John and Jane together can clean the house in 2 hours 24 minutes

                               = 120 + 24

                               = 144 minutes

Let,

          Jane can complete the work alone in x minutes

then,

        Jhon will take (x+120) minutes to complete the same work alone

According to question,

                                    $\frac{1}{x} +\frac{1}{x+120} = \frac{1}{144}$

                                     $\frac{x+120+x}{x(x+120)} =\frac{1}{144}$

                               144(2x+120) = x(x+120)

                      288x + 17280= $x^{2}$ + 120x

                         $x^{2}$ - 168x -17280 = 0

                          (x + 72) (x-240) =0

                             x= -72 and x =240

x can not be negative, so x =240 minute =4 hours

 Jane can complete the work alone in 240minutes = 4 hours

Jhon will take (x+120) minutes to complete the same work

                    x+120

                = 240 + 120

               = 360 minutes = 6 hours

Hence,

           Jhon will take 6 hours to compete the same work

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