Larry Michelle and Turf can finish painting the fence in 2 h

Larry, Michelle and Turf can finish painting the fence in 2 hours. If Michelle does the job alone she can finish it in 5 hours. If Larry does the job alone he can finish it in 6 hours. How long will it take for Turf to finish the job alone?

Solution

Let x hors be the time that Turf takes to paint the fence alone. Michelle , alone can paint the fence in 5 hours, so she can paint 1/5 th of the fence in 1 hour. Similarly, Larry and Turf, working alone, can paint 1/6 and 1/x of the femce in 1 hour. Thus, Michelle, Larry and Turf, working together, can paint 1/5 + 1/6 + 1/x =(6x+ 5x + 30)/30x = (11x + 30) /30x of the fence in 1 hour. Therefore, the three, working together, can paint the fence in 30x/(11x + 30) hours. Then 30x/(11x + 30) = 2 or, 30x = 2(11x + 30) = 22x + 60 or, 30x - 22x = 60 or, 8x = 60 so that x = 60/8 = 15/2 = 7.50 hours.Thus, Turf, alone, can paint the fence in 7.5 hours.