Question

To paint a room it takes mike 75 minutes, Joan 60 minutes, and Kyle 80 minutes when each person works alone. If all three work together how long will the painting take?

Answer 1

60 minutes at max. that is all the info i was given

Answer 2

Mike takes 75 minutes to paint the room. So, in 1 minute the fraction of the room Mike paints is
`(1)/(75)`.

Likewise, in 1 minute the fraction of the room Joan paints is
`(1)/(60)`.

Lastly, in 1 minute the fraction of the room Kyle paints is
`(1)/(80)`.

Now, let
`t` be the number of minutes taken to paint the whole room when all three are working together.

Then, in 1 minute the fraction of the room the three paint will be
`(1)/(t)`.

This can be written as:

`(1)/(t)=(1)/(75)+(1)/(60)+(1)/(80)=(17)/(400)`

Therefore, If all three work together then they will finish the room in:

`t=(400)/(17)\approx 23.53 minutes`