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 together?

John can complete a paper route in 20 minutes.

John's 1 minute work = 1/20, so rate = 1/20 job/minute

Steve can complete the same route in 30 minutes

Steve's 1 minute work = 1/30, so rate = 1/30 job/minute

Together dа ta:

Time = y min/job; Rate = 1/y job/min

rate + rate = together rate

1/20 + 1/30 = 1/y

(30+20) / 600 = 1/y

50/600

5/60 = 1/y

y = 60/5 = 12 minutes (time for this to do the job together)

12 minutes to complete the route together