Question

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?

Answer 1

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.