Questions: Hannah can paint a room in 16 hours. Destiny can paint the same room in 12 hours. How long does it take for both Hannah and Destiny to paint the room if they are working together.

Solution Steps

Person A completes the task at a rate of \(\frac1{16}\) per hour.

Person B completes the task at a rate of \(\frac1{12}\) per hour.

The combined rate is \(\frac1{16} + \frac1{12} = 0.146\) tasks per hour.

The time it takes for both to complete the task together is \(\frac1{0.146} = 6.86\) hours.

Final Answer: It takes 6.86 hours for both Person A and Person B to complete the task together.