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 apint 6 rooms.
Jan's rate = 1 room/ 2/3 hours
Pete's rate = 1 room/ 3/2 hours
combined rate = 1/(2/3) + 1/(3/2)
= 3/2 + 2/3
= 13/6 room/hr
time for 6 rooms = 6 ÷ 13/6
= 6(6/13)
= 36/13 hours or appr 2 hours 46 minutes
btw, painting rooms does not work like that.
3/2 + 2/3 = 9/6 + 4/6 = 13/6
Thank you
To find out how many hours it will take Jan and Pete to paint 6 rooms together, we need to calculate their combined painting rate.
Jan can paint 3 rooms in 2 hours, which means her painting rate is 3 rooms / 2 hours = 1.5 rooms per hour.
Pete can paint 2 rooms in 3 hours, which means his painting rate is 2 rooms / 3 hours = 0.67 rooms per hour (rounded to two decimal places).
To find their combined painting rate, we add their individual rates:
Combined painting rate = Jan's painting rate + Pete's painting rate
= 1.5 rooms per hour + 0.67 rooms per hour
= 2.17 rooms per hour (rounded to two decimal places).
Now, we can calculate the time it will take Jan and Pete to paint 6 rooms by dividing the total number of rooms by their combined painting rate:
Time = Total rooms / Combined painting rate
= 6 rooms / 2.17 rooms per hour
≈ 2.77 hours (rounded to two decimal places).
Therefore, it will take approximately 2.77 hours (or 2 hours and 46 minutes) for Jan and Pete to paint 6 rooms together.
how he got 13/6 room /hr
please explain