Question

Martha can paint a room in $2$ hours.

Jamie can paint the same room in $6$ hours.

How long, to the nearest tenth of an hour, will it take them to paint the room together?

Answer 1

Finding time taken by both of them to paint the room using unitary method:

Martha can paint a room in $2$ hours

Therefore in $1$ hour she can paint $\frac{1}{2}$of the room

Jamie can paint the same room in $6$ hours

Therefore in $1$ hour he can paint $\frac{1}{6}$of the room

Therefore together they can paint $\frac{1}{2}+\frac{1}{6}=\frac{4}{6}=\frac{2}{3}$of the room

$\frac{2}{3}$of the room can be painted in 1 hour

therefore $1$ room can be painted in $\frac{1}{\left({\displaystyle \frac{2}{3}}\right)}=\frac{3}{2}=1.5$hours

Hence, it will take $1.5$ hours for Martha and Jamie to paint the room.