# How long does it take Sergio and Mario to paint the room together? (Assume they are working above the rates if they are working together OR alone) Sergio and Mario are trying to paint the same room. It takes Sergio 8 hours to paint the entire room and it takes Mario 6 hours to paint the entire room.

## Expert Answers

Sergio needs 8 hours to paint a room.

Mario needs 6 hour to paint the room.

We need to find out how long does it take if both were painting the room.

Let us calculate the rate of the painting for 1 hour.

For Sergio:

1 room for 8 hours.

==> 1/8 room for 1 hour...........(1)

For Mario:

1 room for 6 hours

==> 1/6 room for 1 hour...........(2)

Then from (1) and (2), Mario and Sergio can paint 1/8 + 1/6 for one hour.

==> for one hour = 1/6 + 1/8 = 14/48 = 7/24 of the room

7/24 of the room ==> 1 hour

1 room ==> x hours

Cross multiply:

==> x = 24/7 = 3.43 hours

Then, Mario and Sergio needs 3.43 hours to paint the room together.

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