Tina can paint a room in 8 hours, but when she and her friend Emily work together, they can complete the job in 3 hours. How long would it take Emily to paint the room alone?
1/x + 1/8 = 1/3
x = 24/5
To find out how long it would take Emily to paint the room alone, we can first determine how much work they can do together in one hour, and then find out how long it would take Emily to do that same amount of work on her own.
Let's assume Tina's work rate per hour is T (1 room per 8 hours), and Emily's work rate per hour is E (unknown). When they work together, their combined work rate is (T + E) per hour.
According to the given information, when they work together, they can complete the room in 3 hours. So their combined work rate is 1 room per 3 hours, which means (T + E) = 1/3.
Similarly, Tina's work rate on her own is T = 1 room per 8 hours.
Now we can solve these two equations to find E (Emily's work rate):
(T + E) = 1/3 -- (Equation 1)
T = 1/8 -- (Equation 2)
From equation 2, we know that T = 1/8, which means Tina's work rate is 1 divided by 8.
Substituting the value of T into equation 1, we have:
(1/8 + E) = 1/3
To isolate E, we subtract 1/8 from both sides:
E = 1/3 - 1/8
Simplifying this expression, we find:
E = 8/24 - 3/24 = 5/24
Therefore, Emily's work rate is 5/24 rooms per hour.
Now we can find Emily's work time. Since we know her work rate is 5/24 rooms per hour, it will take her 24/5 hours to complete 1 room working alone.
Converting this to a mixed number, it becomes 4 4/5 hours.
Therefore, it would take Emily approximately 4 hours and 48 minutes to paint the room by herself.