Tom, working alone, can paint a room in 6 hours. Peter and

Question

Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?

maratikus · Answer

x - amount of work Tom does in an hour -> x = 1/6
y - amount of work Peter does in an hour -> y = 1/3
z - amount of work John does in an hour -> z = 1/2

total work:
first hour: x
second hour: x + y
the rest of the time (since 2x+y = 2/3 t = (1-2x-y)/(x+y+z)

Peter's work: y + y*t = y*(1+t) = 1/3*(1+(1-1/3-1/3)/(1/6+1/3+1/2)) = 1/3 + 1/9 = 4/9

Tom, working alone, can paint a room in 6 hours. Peter and

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