work and time

Question

Two motor mechanics, Ron and Sam, working together can overhaul a scooter in 6 hours. Ron alone can do the job in 15 hours. In how many hours, can Sam alone do it?

 

PLEASE SHOW ME THE STEPS!!

Answer 1

Let x = number of hours it takes Sam to do the job alone

 

1/15 = portion of job done by Ron per hour if he works alone

 

1/x = portion of job done by Sam per hour if he works alone

 

1/6 = portion of job done per hour if they work together

 

Then, 1/15 + 1/x = 1/6

 

Multiply through by the LCD, 30x, to get 2x + 30 = 5x

 

                                                                   3x = 30

 

                                                                    x = 10 hours

 

Sam can do the job alone in 10 hours.  

 

Answer 2

Ron does 1/15 of the job in 1 hour

Sam takes x # of hours

Sam does 1/x of the job in 1 hour

(1/15)(6)+(1/x)(6)=1 (job finished)

(6/15)+(6/x)=1

multiply all terms on both sides by 15x

6x+90=15x

90=15x-6x

90=9x

x=90/9

x=10 hours for Sam to do the job alone