William and Stephanie are painting the bedrooms in their house. If he had to paint the bedrooms himself, it would take William 4 hours to complete the job. If Stephanie alone were to paint the bedrooms, it would take her 6 hours.Working together, how long will it take William and Stephanie to paint the bedrooms?
Question
William and Stephanie are painting the bedrooms in their house. If he had to paint the bedrooms himself, it would take William 4 hours to complete the job. If Stephanie alone were to paint the bedrooms, it would take her 6 hours.Working together, how long will it take William and Stephanie to paint the bedrooms?
Solution
To solve this problem, we need to find out how much of the painting job William and Stephanie can complete in one hour.
- William can complete the job in 4 hours. Therefore, in one hour, he can complete 1/4 of the job.
- Stephanie can complete the job in 6 hours. Therefore, in one hour, she can complete 1/6 of the job.
Now, if they work together, we can add up the fractions of the job they can complete in one hour.
1/4 (William's work) + 1/6 (Stephanie's work) = 3/12 + 2/12 = 5/12
So, together, they can complete 5/12 of the job in one hour.
To find out how long it will take them to complete the entire job, we divide the whole job (1) by the fraction they can complete in one hour (5/12):
1 ÷ (5/12) = 12/5 = 2.4 hours
So, it will take William and Stephanie 2.4 hours to paint the bedrooms together.
Similar Questions
Alex can paint a wall in 4 hrs. Beth can paint the same wall in 5 hrs. How much time will it take to paint the wall if they work together?
Harry, Annie and Mitch decided to paint the living room.Harry could paint the room by himself in 3 hours.Annie could do it in 4 hours and Mitch would take 6 hours on his own.If they all work together and don't get in each other's way, how long will the job take?
Nancy can paint a fence in 3 hours. It takes Ben 4 hours to do the same job. If they were to work together to paint a fence, approximately how many hours should it take?
If it takes 3 people 2 hours to paint a wall, how long will it take 6 people to paint the same wall, assuming they work at the same rate?
Wendy can build a doghouse in 15 hours, and Miguel can build an identical doghouse in 10 hours. How many hours will it take Wendy and Miguel, working together at their respective constant rates, to build a doghouse?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.