work related problems

Question

Sally and Kim complete a job together in 2 hours. Sally working alone completes the same job in 3 hours less than Kim working alone. How long does it take Kim to complete the job?

Answer 1

Let x = time it takes Kim when she works alone

 

Then, x - 3 = time it takes Sally if she works alone

 

1/x = amount done by Kim each hour

 

1/(x-3) = amount done by Sally in 1 hour

 

1/2 = amount done by both in 1 hour if they work together

 

Then, 1/x + 1/(x-3) = 1/2

 

Multiply by 2x(x-3) to get 2(x-3) + 2x = x(x-3)

 

                                            4x - 6 = x² - 3x

 

                                             x² - 7x + 6 = 0

 

                                            (x-6)(x-1) = 0

 

                                             x = 1 or x = 6

 

If x = 1, then x-3 is negative, which doesn't make sense, since x-3 is the number of hours that it takes for Sally to do the job alone.  

 

So, x = 6 hours