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# Working together at their respective constant rates, Bob and Sam can

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Joined: 02 Sep 2009
Posts: 53063
Working together at their respective constant rates, Bob and Sam can  [#permalink]

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18 Jan 2019, 00:11
00:00

Difficulty:

45% (medium)

Question Stats:

53% (01:41) correct 47% (01:34) wrong based on 39 sessions

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Working together at their respective constant rates, Bob and Sam can mow a lawn in 12 hours. If Bob’s rate is twice Sam’s rate, how many hours would it take Bob, working alone, to mow the lawn?

A 15
B 18
C 24
D 32
E 36

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Working together at their respective constant rates, Bob and Sam can  [#permalink]

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Updated on: 19 Jan 2019, 02:06
Bunuel wrote:
Working together at their respective constant rates, Bob and Sam can mow a lawn in 12 hours. If Bob’s rate is twice Sam’s rate, how many hours would it take Bob, working alone, to mow the lawn?

A 15
B 18
C 24
D 32
E 36

1/b+1/s = 1/12
1/b=2/s
2b=s
we can say
3b/2b^2 = 1/12
solve
we get b= 18
so s = 36
IMO B
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Originally posted by Archit3110 on 18 Jan 2019, 08:42.
Last edited by Archit3110 on 19 Jan 2019, 02:06, edited 1 time in total.
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Re: Working together at their respective constant rates, Bob and Sam can  [#permalink]

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18 Jan 2019, 18:31
1
Working together at their respective constant rates, Bob and Sam can mow a lawn in 12 hours

Bob's work rate is $$\frac{1 (job)}{Bob (hours)}$$
Sam's work rate is $$\frac{1 (job)}{Sam (hours)}$$
Their combined work rate is $$\frac{1 (job)}{Bob (hours)} + \frac{1 (job)}{Sam (hours)} = \frac{1 (job)}{12 (hours)}$$
(see: https://gmatclub.com/forum/combined-rat ... l#p1237427)
Simplify by eliminating units $$\frac{1}{B} + \frac{1}{S}= \frac{1}{12}$$

If Bob’s rate is twice Sam’s rate
So $$\frac{1}{B} = \frac{2}{S}$$ (completes two jobs in the time it takes S to complete 1)

New equation
$$\frac{2}{S} + \frac{1}{S} = \frac{1}{12}$$
$$\frac{3}{S}=\frac{1}{12}$$
Cross multiply
S=36

how many hours would it take Bob, working alone, to mow the lawn?
$$\frac{1}{B}+\frac{1}{36}=\frac{1}{12}$$
$$\frac{36}{36B} + \frac{B}{36B}=\frac{1}{12}$$
$$\frac{36+B}{36B}=\frac{1}{12}$$
Cross multiply
12(36+B)=36B
36+B=3B
36=2B
18=B

Re: Working together at their respective constant rates, Bob and Sam can   [#permalink] 18 Jan 2019, 18:31
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