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?

Question

asked Feb 18, 2019 65.2k views

2 Answers

Gribesh Dhakal · Answer 1 · 2019-02-22T08:36:22+0000

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
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:

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