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It takes John exactly 30 minutes to rake a lawn and it takes his son

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Math Expert

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It takes John exactly 30 minutes to rake a lawn and it takes his son [#permalink]

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21 Jul 2015, 03:23

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Difficulty:

5% (low)

Question Stats:

92% (00:52) correct

8% (01:33) wrong

based on 171 sessions

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It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn?

A. 16
B. 20
C. 36
D. 45
E. 90

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Spoiler: OA

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Re: It takes John exactly 30 minutes to rake a lawn and it takes his son [#permalink]

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21 Jul 2015, 03:27

B.

1/30 + 1/60 = 1/20, hence 20mins for both of them.

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Re: It takes John exactly 30 minutes to rake a lawn and it takes his son [#permalink]

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21 Jul 2015, 03:29

Bunuel wrote:

Time taken by John to rake a lawn = 30 minutes
The work done by John in 1 min = (1/30)

Time taken by John's Son to rake a lawn = 60 minutes
The work done by John's Son in 1 min = (1/60)

The work done by John and his Son in 1 min = (1/30)+(1/60) = (3/60) = (1/20)

i.e. Time taken by John and his Son together to rake (1/20) of Lawn = 1 min
i.e. Time taken by John and his Son together to rake (1) of Lawn = 1/(1/20) = 20 min

Answer: Option B
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Re: It takes John exactly 30 minutes to rake a lawn and it takes his son [#permalink]

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21 Jul 2015, 08:21

Work done by John in 1 minute = 1/30; work done by his son in 1 minute = 1/60.

Time taken to complete the work working together = 1/30 + 1/60 = 90/1800 = 1/20 = 20 minutes. Ans (B).
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Re: It takes John exactly 30 minutes to rake a lawn and it takes his son [#permalink]

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21 Jul 2015, 08:32

Bunuel wrote:

Hi,
two ways..
1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min..
only A and B are left..
if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins..
ans 20 B
2)$\frac{1}{30}+\frac{1}{60}=\frac{1}{20}$
20 mins B
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Re: It takes John exactly 30 minutes to rake a lawn and it takes his son [#permalink]

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21 Jul 2015, 09:59

Bunuel wrote:

1/30 + 1/60 = 3/60 = 1/20

This means it will take 20 minutes to rake the lawn.

B
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Re: It takes John exactly 30 minutes to rake a lawn and it takes his son [#permalink]

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26 Jul 2015, 11:48

Bunuel wrote:

800score Official Solution:

The easiest way to solve work-rate problems is to find a rate per unit of time. If it takes John 30 minutes to rake the lawn, then he can rake 1/30 of the lawn per minute. Todd can rake 1/60 of the lawn per minute. Together they can rake 1/60 + 1/30 = 1/60 + 2/60 = 3/60 = 1/20 of the lawn per minute.

If they rake 1/20 of the lawn per minute, it will take them 20 minutes to rake the lawn together.

The correct answer is choice (B).
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Re: It takes John exactly 30 minutes to rake a lawn and it takes his son [#permalink]

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28 Jul 2015, 21:12

Hi All,

This prompt can also be solved by using the Work Formula:

Work = (A)(B)/(A+B) where A and B are the individual times that it takes to complete the 'job'

We're told that the two 'times to rake a lawn' are 30 minutes and 60 minutes, respectively. We're asked how long it takes to rake the lawn when working together....

(30)(60)/(30+60) = 1800/90 = 20 minutes to complete the task when working together.

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Re: It takes John exactly 30 minutes to rake a lawn and it takes his son [#permalink]

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09 Aug 2017, 12:48

Bunuel wrote:

John’s rate is 1/30 and Todd’s rate is 1/60. We can let t = the time is takes them to complete the lawn together, and thus:

1/30 + 1/60 = 1/t

Multiplying by 60t, we have:

2t + t = 60

3t = 60

t = 20

Answer: B
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