How do we solve the problem below?

Question

John can complete a paper route in 20 minutes.  Steve can complete the same route in 30 minutes. How long will it take them to complete the route if they work togther?

Answer 1

John completes 1/20 of the job in 1 minute

Steve completes 1/30 of the job in 1 minute

x=# of minutes working together to complete the job

(1/20)(x)+(1/30)(x)=1 (job completed)

multiply both side by the LCM which is 60

(60)(1/20)(x)+(60)(1/30)(x)=(60)(1)

3x+2x=60

5x=60

x=60/5

x=12 minutes