Ryan is building a tree house. It will take 84 1/4 hours to complete the tree house. He can work 15 1/2 hours each week . To the nearest tenth, how many weeks will it take Ryan to complete the tree house?
(84 1/4) / (15 1/2)
(337/4) / (31/2)
337/4 * 2/31
337/62
...
To find the number of weeks it will take Ryan to complete the tree house, we need to divide the total number of hours needed to complete the tree house by the number of hours Ryan can work each week.
First, let's convert the mixed numbers into improper fractions:
- 84 1/4 hours = 84 + 1/4 = 84 * 4/4 + 1/4 = (336/4) + (1/4) = 337/4 hours
- 15 1/2 hours = 15 + 1/2 = 15 * 2/2 + 1/2 = (30/2) + (1/2) = 31/2 hours
Now, we can divide the total number of hours needed by the number of hours Ryan can work each week:
(337/4) ÷ (31/2) = (337/4) * (2/31)
To multiply fractions, we multiply the numerators and denominators separately:
(337 * 2) / (4 * 31) = 674 / 124
To find the number of weeks, we need to divide the total hours it will take to complete the tree house by the number of hours Ryan can work each week:
674 / 124 ≈ 5.44
Therefore, it will take Ryan approximately 5.4 weeks (rounded to the nearest tenth) to complete the tree house.