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# If Johnny can mow the lawn in 30 minutes and with the help of his brot

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If Johnny can mow the lawn in 30 minutes and with the help of his brot  [#permalink]

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10 Oct 2017, 18:12
1
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Difficulty:

5% (low)

Question Stats:

86% (01:27) correct 14% (01:21) wrong based on 49 sessions

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If Johnny can mow the lawn in 30 minutes and with the help of his brother, Bobby, they can mow the lawn 20 minutes, how long would it take Bobby working alone to mow the lawn?

(A) 1/2 hour

(B) 3/4 hour

(C) 1 hour

(D) 3/2 hours

(E) 2 hours

SOURCE: NOVA GMAT

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Re: If Johnny can mow the lawn in 30 minutes and with the help of his brot  [#permalink]

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10 Oct 2017, 20:18
fitzpratik wrote:
If Johnny can mow the lawn in 30 minutes and with the help of his brother, Bobby, they can
mow the lawn 20 minutes, how long would it take Bobby working alone to mow the lawn?

(A) 1/2 hour

(B) 3/4 hour

(C) 1 hour

(D) 3/2 hours

(E) 2 hours

SOURCE: NOVA GMAT

hi..

two ways -

J's one minute work = $$\frac{1}{30}$$
B's and J's combined 1 minute work = $$\frac{1}{20}$$

so B's one minute work = $$\frac{1}{20}-\frac{1}{30} = \frac{3-2}{60} = \frac{1}{60}$$
so time taken will be 60 minutes or 1 hour

logical way..
J can complete the work in 30 minutes so he does 20/30 of the work in 20 minutes

the remaining work $$1-\frac{20}{30}=\frac{1}{3}$$ is done by B in 20 minute ..
so he will do comlete work in 20*3=60 minute or 1 hour

C
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Re: If Johnny can mow the lawn in 30 minutes and with the help of his brot  [#permalink]

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10 Oct 2017, 20:36
Let the work done by Bobby in 1 min=$$\frac{1}{x}$$
work done by Johnny in 1 min= $$\frac{1}{30}$$

Work done by both of them together:
$$\frac{1}{30}$$+$$\frac{1}{x}$$= $$\frac{1}{20}$$

$$\frac{1}{x}$$= $$\frac{1}{20}$$-$$\frac{1}{30}$$

=$$\frac{3-2}{60}$$= 1/60

So time taken by Bobby working alone= 60 mins or 1 hour

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Re: If Johnny can mow the lawn in 30 minutes and with the help of his brot  [#permalink]

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10 Oct 2017, 21:37
Let the work required in mowing the lawn = LCM of 30 & 20 = 60 units

Johnny alone does in 30 minutes, so Johnny can do 60/30 = 2 units per minute
Together, they can do in 20 minutes, so Johnny + Bobby together can do = 60/20 = 3 units per minute

Now, J does 2 units, and they both 3 units, so Bobby's per minute work = 3-2 = 1 unit

So time taken by Bobby alone = 60/1 = 60 minutes

Re: If Johnny can mow the lawn in 30 minutes and with the help of his brot &nbs [#permalink] 10 Oct 2017, 21:37
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