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?
Tina can paint 1/8 of a room in one hour.
Tina and Emily can paint 1/3 of a room in one hour.
So Emily can paint (1/3-1/8)=5/24 of a room in one hour.
It therefore takes Emily 1/(5/24)=24/5 hours to paint a room
4.8 hours
To find out how long it would take Emily to paint the room alone, we can use the concept of rates. Let's denote Tina's painting rate as "T" (which is the fraction of the room she can paint in one hour) and Emily's painting rate as "E" (the fraction of the room Emily can paint in one hour).
From the given information, we know that Tina can paint the entire room in 8 hours, so Tina's painting rate is 1/8th of the room per hour, i.e., T = 1/8.
When Tina and Emily work together, the two rates combine, so their combined painting rate is (T + E) = 1/3, as they can complete the room in 3 hours.
Now, we need to find the painting rate of Emily (E) to determine how long it would take her to paint the room alone.
We can subtract Tina's rate (1/8) from the combined rate (1/3) to find Emily's rate:
(T + E) - T = E = 1/3 - 1/8
To simplify the subtraction, we need a common denominator for both fractions, which is 24:
E = 8/24 - 3/24
E = 5/24
Therefore, Emily's painting rate is 5/24 of the room per hour. This means she can paint 5/24th of the room in one hour.
To determine how long it would take Emily to paint the entire room alone, we can calculate the reciprocal of Emily's painting rate:
1 / (5/24) = 24/5 = 4.8
So, it would take Emily approximately 4.8 hours (or 4 hours and 48 minutes) to paint the room alone.