Algebra wordplroblem - Time- Equations

Question

Working together, two workmen take 14 hours to complete a job. How much time would it take them to complete it separately if one of the workmen is two times faster than the other?

I need the answer in equation form, not in words.

Thank you so much!!

Answer 1

the fast workman takes x hours to complete the job

the slow workman takes 2x hours to complete the job

the fast worker does 1/x of the job in 1 hour   (his rate per hour)

the slow worker does 1/2x of the job in 1 hour   (his rate per hour)

together it takes them 14 hours to complete the job

set up an equation...

(1/x)(14)+(1/2x)(14)=1  (job finished)

(14/x)+(14/2x)=1

(14/x)+(7/x)=1

multiply both sides by x

x(14/x)+x(7/x)=x(1)

14+7=x

21=x

x=21 hours for the fast worker

2x=42 hours for the slow worker