Painting Trio

[vtsanders]

This is #2 from the WT question bank:
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?

Im a little confused about the reasoning here. If Tom complete 1/3 of the job in 1 hour by himself. How does Peter and Tom, working together, complete 1/2 of the same job IF Tom has already finished 1/3 of it? Would they have not completed 5/12 (5/6 remaining *1/2)?

Maybe my reasoning is wrong, I dont know.

[mithunsam]

Interesting question... Let us see...

Tom takes 6 hours to complete the work => Tom completes 1/6th of the work in 1 hour
Pete takes 3 hours to complete the work => Pete completes 1/3rd of the work in 1 hour
John takes 2 hours to complete the work => John completes 1/2 of the work in 1 hour

Question says that Tom worked first 1 hour alone. So, 1/6th of the work is complete and 5/6th is pending.

Now Pete joined Tom.
Let us calculate how much time it would take for Pete and Tom together to complete the original work
1/6 + 1/3 = 1/h
1/2 = 1/h
or h = 2 hours

Both of them together can complete the original work in 2 hours. That means, they can complete 1/2 of the original work in 1 hour. [answer for your question].

However, Pete is twice as fast as Tom. That means, Pete completed 2/3 * 1/2 of original work = 1/3)

Now the pending work is 1 - (1/2 + 1/6) = 1 - 2/3 = 1/3. Tom, Pete and John worked together to finish the last 1/3 of the work. Pete is only 1/3rd as fast as Tom & John combined. So, the amount of work done by Pete is 1/3 * 1/3 = 1/9.

Total work done by Pete = 1/3 + 1/9 = 4/9

Is it the correct answer?

[tim]

4/9 is correct; nice job..

[rkafc81]

how would you solving this one using Ron's 7-step RTD/RTW approach (see Thursday's with Ron video on Rates etc.)

??

I tried to do it that way but got stuck on the amount of work done during each step of the process...

let x be the total amount of work done
i.e. stage 1 (Tom only) : 1/3x
stage 2(Tom + Peter) : 1/2x
stage 3(Tom + Peter + John): x

... obviously i didnt see here by this stage that all their work already added up to more than x !!

but yeah, how would you do this that way?

[tim]

if you want to ask about a specific solution method, please describe the method in detail for the benefit of the other readers of this forum..