Jan and Pete are home decorators. Jan can paint 3 rooms in 2 hours. Pete can paint 2 rooms in 3 hours. If they work together, about how many hours will it take Jan and Pete to paint 6 rooms?
Jan's rate = 3/2 rooms/hr
Pete's rate = 2/3 rooms/hr
combined rate = 3/2 + 2/3 rooms/hr = 16/6 rooms/hr
time to do 1 room at combined rate = 1/(16/6) hrs = 6/16 or 3/8 hrs
so to do 6 rooms would take 6(3/8) hours
= 9/4 hrs or 2 hours and 15 minutes
Jan's rate = 3/2 rooms/hr
Pete's rate = 2/3 rooms/hr
combined rate = 3/2 + 2/3 rooms/hr = 16/6 rooms/hr
time to do 1 room at combined rate = 1/(16/6) hrs = 6/16 or 3/8 hrs
so to do 6 rooms would take 6(3/8) hours
so = 9/4 hrs or 2 hours and 15 minutes
To find out how many hours it will take Jan and Pete to paint 6 rooms together, we need to calculate their combined rate of work.
Let's calculate Jan's rate of work first. Jan can paint 3 rooms in 2 hours, so her rate of work is 3 rooms / 2 hours = 1.5 rooms per hour.
Next, let's calculate Pete's rate of work. Pete can paint 2 rooms in 3 hours, so his rate of work is 2 rooms / 3 hours = 0.67 rooms per hour.
To find their combined rate of work, we can simply add their individual rates of work. So, Jan and Pete's combined rate of work is 1.5 rooms per hour + 0.67 rooms per hour = 2.17 rooms per hour.
Now, we can use this combined rate of work to find the time it will take Jan and Pete to paint 6 rooms. Since their rate of work is 2.17 rooms per hour, the time it will take to paint 6 rooms is 6 rooms / 2.17 rooms per hour = 2.77 hours (rounded to the nearest hundredth).
Therefore, it will take Jan and Pete approximately 2.77 hours to paint 6 rooms together.