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

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Math Expert
Joined: 02 Sep 2009
Posts: 58465
Working together at their respective constant rates, Bob and Sam can  [#permalink]

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18 Jan 2019, 01:11
00:00

Difficulty:

45% (medium)

Question Stats:

55% (01:34) correct 45% (01:41) wrong based on 98 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, 03:06
1
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

Originally posted by Archit3110 on 18 Jan 2019, 09:42.
Last edited by Archit3110 on 19 Jan 2019, 03:06, edited 1 time in total.
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Joined: 15 Feb 2018
Posts: 372
Re: Working together at their respective constant rates, Bob and Sam can  [#permalink]

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18 Jan 2019, 19:31
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

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

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03 Mar 2019, 16:28
B+S t is = 12 to complete Work = 1, so their combined rate is 1/12
B's rate is twice that of S, so B=2r, S=r (note this means B does twice as much work as S for t=1)
combined rates: 1/12 = 3r ---> 1/36 = r
B working alone is 2(1/36) = 1/18 rate, so Work(1) / 1/18 ---> t = 18
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Posts: 20
Re: Working together at their respective constant rates, Bob and Sam can  [#permalink]

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13 May 2019, 08:49
I always put on the top of my sheet the formula W=R*t

then I say:

Names-------W-------------R------------t

B+S---------1--------------1/12---------12h

B------------1--------------2x------------?

S------------1---------------x------------?

then, as we can sum up rates, 2x + x = 1/12 ---> x= 1/36
thus, B's rate = 1/18. Therefore, reversing the rate I will obtain the time. 18h -->(B)
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Posts: 1224
Re: Working together at their respective constant rates, Bob and Sam can  [#permalink]

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13 May 2019, 09:21
1
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

in 12 hours Bob mows 2/3 lawn
12/(2/3)=18 hours for Bob to mow lawn alone.
18
B
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Re: Working together at their respective constant rates, Bob and Sam can  [#permalink]

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13 May 2019, 13:44
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

Note: Bob’s rate is twice Sam’s rate.

Thus if bob needs x days to complete a work , sam needs 2x days to do so.

1/x + 1/2x = 1/12

3/2x = 1/12

x = 18.

Re: Working together at their respective constant rates, Bob and Sam can   [#permalink] 13 May 2019, 13:44
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