Hannah can paint a room in 8 hours. Destiny can paint the same room in 10 hours. How long does it take for both

Hannah and Destiny to paint the room it they are working together.

Answer:it will take both of the 4.44 hours.

Step-by-step explanation:

Hannah can paint a room in 8 hours. This means that the rate at which she paints the room per hour is 1/8

Destiny can paint the same room in 10 hours. This means that the rate at which Destiny paints the room per hour is 1/10

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be

1/8 + 1/10 = 9/40

Assuming it takes t hours for both of them to paint the room working together, their working rate per hour would be 1/t. Therefore,

9/40 = 1/t

t = 40/9 = 4.44 hours

Step-by-step explanation:

Let x = time (hours) it takes for both

then

x (1/8 + 1/6) = 1

multiplying both sides by 24 (common denominator):

x (3 + 4) = 24

x (7) = 24

x = 24/7

x = 3.429 hours

or

x = 3 hours and 26 minutes