The first painter can finish a paint job in 2 hours. The second painter can finish the same job in 8 hours. How long would it take them to finish the job if they were working together?
We can use the formula:
time = work / rate
where work is the amount of work to be done (in this case, one paint job) and rate is the rate of work of each painter (in terms of jobs per hour). Then, the time it takes for both painters to finish the job working together is simply the sum of the time it takes each painter working alone. Let's apply this formula to each painter:
First painter:
rate = 1 job / 2 hours = 0.5 jobs/hour
Second painter:
rate = 1 job / 8 hours = 0.125 jobs/hour
Working together:
rate = (rate of first painter) + (rate of second painter) = 0.5 jobs/hour + 0.125 jobs/hour = 0.625 jobs/hour
Then, using the formula:
time = work / rate = 1 job / 0.625 jobs/hour = 1.6 hours
Therefore, it would take both painters working together 1.6 hours (or approximately 1 hour and 36 minutes) to finish the job.