How long would of it taken Homer

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 6 hours until Homer had to go home. Mike finished the job working by himself in an additional 6 hours. How long would it have taken Homer to fix the deck himself?

Answer 1

Hi Rhonda,

 

Let x = time it takes homer to complete the job

 

x -1 = time it takes mike to complete the job

 

homers rate = 1/x        This is the fraction that Homer completes in one hour

 

Mike's rate = 1/(x-1)   This is the fraction that mike completes in one hour

 

We know that they worked together for 6 hours and then Mike worked 6 hours more

 

so

 

6(1/x) + 6(1/(x-1)) + 6(1/(x-1))  = 1        This is the time * rate for each person  and it must total one

 

multiply by x(x-1) to get rid of fractions

 

6x -6 + 6x + 6x = x(x-1)

 

18x - 6 = x² - x

 

0 = x² -19x + 6

 

Use the quadratic formula

 

x = 18.67878                       Homer's time to do it alone

 

x -1 = 17.67878                    Mike's time to do it alone

 

Hope this helps