Question

Homer and Mike were replacing the boards on​ Mike's old deck. Mike can do the job alone in 1 hour less time than Homer. They worked together for 4 hours until Homer had to go home. Mike finished the job working by himself in an additional 3 hours. How long would it have taken Homer to fix the deck​ himself?

It will take Homer approximately _______ hours ___________minutes to fix the deck by himself.

​(Round to the nearest minute as​ needed.)

Answer 1

Let x is the time for homer alone to do one job

So (x-1) for Mike alone to do job.

So rate of Homer doing a job is 1/x

Rate of Mike doing a job is 1/(x-1)

Homer and Mike do work together for 3 hours.

So amount of work done is

Mike finished the work by himself additional 3 hours.

So Mike finished the remaining part of job i.e

So sum of both these part make a sum of 1 whole job.

     

     

       

         

We will leave 0.30958 hours because it is less than 1.

So x = 5 + 4.69042 = 9.69042 hours

So Homer will take approximately 9 hours and 41 minutes to fix the deck by himself.