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A father and a son work together to shovel snow off their driveway, th

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A father and a son work together to shovel snow off their driveway, th  [#permalink]

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New post 25 Nov 2018, 08:17
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Question Stats:

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A father and a son work together to shovel snow off their driveway, they can shovel all of the snow in 24 minutes. If the son works alone it takes him 20 more minutes to shovel the driveway than the father when the father shovels alone. How long does it take the father to shovel the driveway alone?

A. 12 minutes

B. 40 minutes

C. 72 minutes

D. 96 minutes

E. 120 minutes
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Joined: 02 Aug 2009
Posts: 7106
Re: A father and a son work together to shovel snow off their driveway, th  [#permalink]

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New post 11 Dec 2018, 21:36
4
deddex wrote:
Jazzmin wrote:
A father and a son work together to shovel snow off their driveway, they can shovel all of the snow in 24 minutes. If the son works alone it takes him 20 more minutes to shovel the driveway than the father when the father shovels alone. How long does it take the father to shovel the driveway alone?

A. 12 minutes

B. 40 minutes

C. 72 minutes

D. 96 minutes

E. 120 minutes


Any easier way to solve this OR is this the only way? chetan2u VeritasKarishma generis (I did a mistake while calculating this twice...also find this calculation a bit time consuming)



Hi...
A very simple way is to use the choices to advantage..
Remember, if two person work at same speed, the time taken will be half of what each takes.
So if A and B both take 20 minutes each working alone, they will finish the work in 20/2 or 10 minutes working together.


Ok .

They work together to finish in 24 minutes, so
(I) each would take more than 24 minutes when working alone...

Also son takes more time than father..
(II) if both were of same speed, both would have taken 48 minutes. But since father is faster than son, so father will take less than 48 minutes and son will take more than 48 minutes.


So father's time is between 24 and 48. Only B fits in

B
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A father and a son work together to shovel snow off their driveway, th  [#permalink]

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New post Updated on: 26 Nov 2018, 18:47
Jazzmin wrote:
A father and a son work together to shovel snow off their driveway, they can shovel all of the snow in 24 minutes. If the son works alone it takes him 20 more minutes to shovel the driveway than the father when the father shovels alone. How long does it take the father to shovel the driveway alone?

A. 12 minutes

B. 40 minutes

C. 72 minutes

D. 96 minutes

E. 120 minutes


Let father alone takes x minutes,
Then son alone takes (x+20) minutes,

As both together takes 24 minutes

Equating work done per minute,
We have

1/x + 1/(x+20) = 1/24
=>(x+20+x)/(x(x+20)) = 1/24
=> 24(2x+20) = x(x+20)
=> 48x + 480 = x^2 +20x
=> x^2 - 28x - 480 =0
=> (x-40)(x+12) = 0
=> x = 40 or x = -12

As x can't be negative, x = 40
Answer choice B

Posted from my mobile device

Originally posted by v12345 on 25 Nov 2018, 09:10.
Last edited by v12345 on 26 Nov 2018, 18:47, edited 2 times in total.
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Re: A father and a son work together to shovel snow off their driveway, th  [#permalink]

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New post 26 Nov 2018, 18:43
Let time taken by father = x
Time takes by son = x+20

R = 1/T and R = R1 + R2
1/x + 1/x+20 = 1/24

Equating, we get X = 40.

Time taken by father = 40 minutes.
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Re: A father and a son work together to shovel snow off their driveway, th  [#permalink]

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New post 08 Dec 2018, 15:40
1
Jazzmin wrote:
A father and a son work together to shovel snow off their driveway, they can shovel all of the snow in 24 minutes. If the son works alone it takes him 20 more minutes to shovel the driveway than the father when the father shovels alone. How long does it take the father to shovel the driveway alone?

A. 12 minutes

B. 40 minutes

C. 72 minutes

D. 96 minutes

E. 120 minutes


Let f be the time the father alone takes to shovel the driveway. Then we have 1/f + 1/(f+20) = 1/24 . Now you can do a lot of tedious and more importantly time consuming algebra. Instead we should work with the answer choices: We can eliminate A right off the bet, since 1/12 is greater than 1/24. We can eliminate D and E by approximating 1/100+1/100= 1/50. That is not even close to 1/24. Then we can approximate 1/80+1/80=1/40 for answer choice C. This only leaves B as our solution by process of elimination.
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A father and a son work together to shovel snow off their driveway, th  [#permalink]

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New post 11 Dec 2018, 12:25
v12345 wrote:
Jazzmin wrote:
A father and a son work together to shovel snow off their driveway, they can shovel all of the snow in 24 minutes. If the son works alone it takes him 20 more minutes to shovel the driveway than the father when the father shovels alone. How long does it take the father to shovel the driveway alone?

A. 12 minutes

B. 40 minutes

C. 72 minutes

D. 96 minutes

E. 120 minutes


Let father alone takes x minutes,
Then son alone takes (x+20) minutes,

As both together takes 24 minutes

Equating work done per minute,
We have

1/x + 1/(x+20) = 1/24
=>(x+20+x)/(x(x+20)) = 1/24
=> 24(2x+20) = x(x+20)
=> 48x + 480 = x^2 +20x
=> x^2 - 28x - 480 =0
=> (x-40)(x+12) = 0
=> x = 40 or x = -12

As x can't be negative, x = 40
Answer choice B

Posted from my mobile device


Any easier way to solve this OR is this the only way? chetan2u VeritasKarishma generis (I did a mistake while calculating this twice...also find this calculation a bit time consuming)
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Re: A father and a son work together to shovel snow off their driveway, th  [#permalink]

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New post 11 Dec 2018, 21:28
deddex wrote:
v12345 wrote:
Jazzmin wrote:
A father and a son work together to shovel snow off their driveway, they can shovel all of the snow in 24 minutes. If the son works alone it takes him 20 more minutes to shovel the driveway than the father when the father shovels alone. How long does it take the father to shovel the driveway alone?

A. 12 minutes

B. 40 minutes

C. 72 minutes

D. 96 minutes

E. 120 minutes


Let father alone takes x minutes,
Then son alone takes (x+20) minutes,

As both together takes 24 minutes

Equating work done per minute,
We have

1/x + 1/(x+20) = 1/24
=>(x+20+x)/(x(x+20)) = 1/24
=> 24(2x+20) = x(x+20)
=> 48x + 480 = x^2 +20x
=> x^2 - 28x - 480 =0
=> (x-40)(x+12) = 0
=> x = 40 or x = -12

As x can't be negative, x = 40
Answer choice B

Posted from my mobile device


Any easier way to solve this OR is this the only way? chetan2u VeritasKarishma generis (I did a mistake while calculating this twice...also find this calculation a bit time consuming)


I guess Zoom96 's POE works amazingly well here, Thank you so much
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Re: A father and a son work together to shovel snow off their driveway, th  [#permalink]

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New post 12 Dec 2018, 00:07
1
deddex wrote:
v12345 wrote:
Jazzmin wrote:
A father and a son work together to shovel snow off their driveway, they can shovel all of the snow in 24 minutes. If the son works alone it takes him 20 more minutes to shovel the driveway than the father when the father shovels alone. How long does it take the father to shovel the driveway alone?

A. 12 minutes

B. 40 minutes

C. 72 minutes

D. 96 minutes

E. 120 minutes


Let father alone takes x minutes,
Then son alone takes (x+20) minutes,

As both together takes 24 minutes

Equating work done per minute,
We have

1/x + 1/(x+20) = 1/24
=>(x+20+x)/(x(x+20)) = 1/24
=> 24(2x+20) = x(x+20)
=> 48x + 480 = x^2 +20x
=> x^2 - 28x - 480 =0
=> (x-40)(x+12) = 0
=> x = 40 or x = -12

As x can't be negative, x = 40
Answer choice B

Posted from my mobile device


Any easier way to solve this OR is this the only way? chetan2u VeritasKarishma generis (I did a mistake while calculating this twice...also find this calculation a bit time consuming)


Also, you can use options to plug in and see what works (if the brilliant logic given by chetan2u above doesn't come to mind)

\(\frac{1}{x} + \frac{1}{(x+20)} = \frac{1}{24}\)

Since x must be positive, if we put x = 12, the first term itself will be greater than 1/24.
So try x = 40

\(\frac{1}{x} + \frac{1}{(x+20)} = \frac{1}{40} + \frac{1}{(40+20)} = \frac{1}{24}\)
This works.
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Re: A father and a son work together to shovel snow off their driveway, th  [#permalink]

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New post 12 Dec 2018, 00:50
Really appreciate chetan2u & VeritasKarishma for the invaluable insight and time saving methods!
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Re: A father and a son work together to shovel snow off their driveway, th &nbs [#permalink] 12 Dec 2018, 00:50
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