Peter can paint a room in 5 hours, Paul can paint a room in 6 hours, Neil can paint a room in 7 1/2 hours and Mary can paint a room in 3 3/4 hours.

Question

Which two painters above can team up to paint a whole room in 3 hours?

Write and solve a Rational Equation that shows you are correct. Please show your work.

Answer 1

Start with Peter and Paul: t/5 + t/6 = 1 30 is the LCD so 6t +5t = 30 t =30/11 t= 2.73 hr Now look at Peter and Neil t/5 + t/15/2 = 1 t/5 +2t/15 = 1 15 is the LCD so 3t + 2t = 15 5t = 15 t =3 hr Peter and Mary t/5 +t/15/4 =1 t/5 + 4t/15 +1 15 is the LCD so 3t + 4t = 15 7t = 15 t= 2.14 hr Paul and Neil t/6 + 2t/15 = 1 LCD is 30 so 5t + 4t = 30 9t = 30 t= 3.33 hr Paul and Mary t/6 + 4t/15 =1 LCD is 30 5t + 8t =30 13t = 30 t= 2.3 hr Neil and Mary 2t/15 + 4t/15 =1 6t = 15 t= 2.5 hr So the team that can paint a room in 3 hr is Peter and Neil.