Hannah can paint a room in 12 hours. Destiny can paint the same room in 20 hours. How long does it take for both Hannah and Destiny to paint the room if they did it together?

The answer to your question is 7:30 h

Step-by-step explanation:

Data

Hanna paints in 12 h

Destiny paints in 20 h

Together = ?

Process

1.- Calculate the amount that each girl paints in 1 hour

Hanna will paint 1/12 in 1 hour

Destiny will paint 1/20 in 1 hour

2.- Write an equation to solve this problem

                      1/12 t + 1/20 t = 1

t = time (h)

1 is when the room is painted 100%.

3.- Solve the equation for t

                    (5 + 3)t/60 = 1

                          8t = 60

                            t = 60/8

                            t = 7.5 h

4.- Conclusion

They will paint the room together in 7:30 h                

It will take 7.5 hours

Step-by-step explanation:

Hannah can paint a room in 12 hours. This means that the rate at which she paints per hour is 1/12

Destiny can paint the same room in 20 hours This means that the rate at which Destiny can paint the same room is 1/20

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

1/12 + 1/20 = 8/60

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

8/60 = 1/t

t = 60/8

t = 7.5 hours