Question

Room has two doors. Door A will empty the room in 14 minutes. Door B will empty the room in 29 minutes. In what time will the room be empty if both doors are open?

Answer 1

Solution :

Door A empties the room in 14 minutes;

In 1 minute, it empties $1 \over 14$ of the room.

Door B empties the room in 29 minutes;

In 1 minute, it empties $1 \over 29$ of the room.

Therefore, in 1 minute, the 2 doors together empty

$${1 \over 14}+{1 \over 29}={43 \over 406}$$

Of the room.

To empty the entire room, it will thus take:

$${1 \over {43 \over 406}}={406 \over 43}=9.4418minutes$$

Answer: 9.4418 minutes