Hannah can paint a room in 20 hours. Destiny can paint the same room in 16 hours. How long does it take for both Hannah and Destiny to paint the room it they are working together.

amount of room hannah can paint in an hour = 1/20
amount of room destiny can paint in an hour = 1/16
number of hours = x

1/20x + 1/16x = 1
the reason why this formula is true is, the amount of the room painted in the end should be 1 (the whole room)

4/80x + 5/80x = 1
9/80x = 1
9x = 80
x = 80/9 hours
x = 8.89 hours

Answer Link

topeadeniran2 topeadeniran2 · Answer 2 · 2021-10-26T06:30:52-04:00

The number of hours that it will take for both Hannah and Destiny to paint the room when they are working together is 9 8/9 hours.

Based on the information given, the fraction that can be painted by Hannah in an hour will be 1/20.

The fraction that can be painted by Destiny in an hour will be 1/16.

Therefore, the formula to solve the question will be:

1/20x + 1/16x = 1/1

4x + 5x = 80

9x = 80

Divide both side by 9

9x/9 = 80/9

x = 8 8/9 hours.

Therefore, it'll take them 8 8/9 hours to paint the room.

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