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# If Bob, working alone, can paint a certain room in 3 hours, how long

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Math Expert
Joined: 02 Sep 2009
Posts: 50623
If Bob, working alone, can paint a certain room in 3 hours, how long  [#permalink]

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28 Mar 2016, 01:30
00:00

Difficulty:

5% (low)

Question Stats:

89% (00:48) correct 11% (00:50) wrong based on 135 sessions

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If Bob, working alone, can paint a certain room in 3 hours, how long does it take Bob and Richard working together to paint the room?

(1) Richard, working alone, can paint the room in 2 hours.

(2) Richard paints at a constant rate that is 50% greater than the rate at which Bob paints.

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If Bob, working alone, can paint a certain room in 3 hours, how long  [#permalink]

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28 Mar 2016, 03:00
Time taken by Bob to paint room, Tb = 3hours
Time needed by both Bob and Richard working together to paint room, Tbr = ?
Work done by Bob in 1 hour = 1/3
To calculate the Tbr we need the time taken by Richard to paint the room . Using this time we can calculate the rate
at which work in done by Richard .
Time = Total Work /Rate

(1) Richard, working alone, can paint the room in 2 hours.
Sufficient
Time taken by Richard to paint room , Tr = 2hours
(The below calculation is not necessary )
Work done by Richard in 1 hour = 1/2
Total work done by Richard and Bob in 1 hour = 1/2 + 1/3 = 5/6
Total time needed , Tbr = 6/5 hour

(2) Richard paints at a constant rate that is 50% greater than the rate at which Bob paints.
Work done by Bob in 1 hour = 1/3
=> Work done by Richard in 1 hour = (3/2)*(1/3) = 1/2
Sufficient

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Re: If Bob, working alone, can paint a certain room in 3 hours, how long  [#permalink]

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01 Aug 2016, 03:08
1
Bunuel wrote:
If Bob, working alone, can paint a certain room in 3 hours, how long does it take Bob and Richard working together to paint the room?

(1) Richard, working alone, can paint the room in 2 hours.

(2) Richard paints at a constant rate that is 50% greater than the rate at which Bob paints.

From stimulus we know bob's rate
We are asked to find bob's rate + richard rate

AIM:- Look out for Richard's rate

(1) Richard, working alone, can paint the room in 2 hours.
Bingo !! :- Thats what we were looking for
SUFFICIENT

(2) Richard paints at a constant rate that is 50% greater than the rate at which Bob paints.
Ok !! Richard is 50% faster than Bob ..Bob's rate is 3
so we can find Richards rate also that is 4.5
SUFFICIENT

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Re: If Bob, working alone, can paint a certain room in 3 hours, how long  [#permalink]

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10 Oct 2017, 06:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If Bob, working alone, can paint a certain room in 3 hours, how long &nbs [#permalink] 10 Oct 2017, 06:03
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