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# Working together, Wayne and his son can shovel the entire

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Joined: 19 Feb 2010
Posts: 351
Working together, Wayne and his son can shovel the entire  [#permalink]

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17 Sep 2010, 03:03
4
5
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:25) correct 25% (01:40) wrong based on 232 sessions

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Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel three times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?

A. 4
B. 6
C. 8
D. 9
E. 12
Intern
Joined: 18 Jul 2010
Posts: 44

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17 Sep 2010, 03:31
W: the time for Wyane to do the job
S: the time for his son to do the job

We have 1/W + 1/S = 1/3 and W = 3S

Then we have 1/(3*S) + 1/S = 1/3 <=> 4/(3*S) = 1/3 <=> S = 12

ANS: E
Manager
Joined: 30 Aug 2010
Posts: 88
Location: Bangalore, India

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29 Sep 2010, 04:57
1
Wayne works 3 times as fast as his son does and both together compltes the work in 3 days ===> 4sons [(1son) + (father=3sons)] complete the work in 3 days ===> 1 son compltes the work in 3*4 days t.e 12 days
Manager
Joined: 22 Jan 2012
Posts: 82
Location: India
Concentration: General Management, Technology
GPA: 3.3
WE: Engineering (Consulting)

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13 Mar 2012, 06:13
2
son+wayne combined rate = 1/3
if son takes 3s hours then wayne takes s hours
so 1/3s(son) + 1/s(wayne) = 1/3 ==> s = 4
so son will take 3s hours i.e 12 hours so E is the correct answer
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Joined: 20 Feb 2012
Posts: 32
Re: Working together, Wayne and his son can shovel the entire  [#permalink]

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13 Mar 2012, 08:34
(e)
LET WAYNE WORK RATE = W
HIS SON'S WORK RATE = S

GIVEN 1/W + 1/S = 1/3
ALSO W=3S

=> 1/3S + 1/S = 1/3 => 1+3/S = 1/3

=>BY SOLVING WE GET S = 12
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Joined: 03 Aug 2010
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Re: Working together, Wayne and his son can shovel the entire  [#permalink]

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17 Apr 2012, 22:14
How to get the equations right?

We are supposed to find out Time taken by son,s=?

time taken by wayne =w = 3s
time taken by son= s

WS/W+S = 3
3s^2/4s = 3
3s^2 = 12s
Cancelling common s on both sides
3s=12
s=4
w=12

hmmm. I know that wayne works at a faster rate and so wayne's time taken should be less than his son. However can you please tell me what mistake I am making in the above equations? I am sure there is a high possibility I will pick answer as 4 during the exam if I have to form the equations as above.
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Re: Working together, Wayne and his son can shovel the entire  [#permalink]

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17 Apr 2012, 22:31
2
ENAFEX wrote:
Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel three times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?

A. 4
B. 6
C. 8
D. 9
E. 12

How to get the equations right?

We are supposed to find out Time taken by son,s=?

time taken by wayne =w = 3s
time taken by son= s

WS/W+S = 3
3s^2/4s = 3
3s^2 = 12s
Cancelling common s on both sides
3s=12
s=4
w=12

hmmm. I know that wayne works at a faster rate and so wayne's time taken should be less than his son. However can you please tell me what mistake I am making in the above equations? I am sure there is a high possibility I will pick answer as 4 during the exam if I have to form the equations as above.

Wayne can shovel three times as fast as his son can. So, if Wayne needs W hours then his son needs 3W hours (more hours than Wayne). Or if the son needs S hour than Wayne needs S/3 hours (less hours than his son).

1/w+1/(3w)=1/3 --> w=4 --> s=3w=12.

Hope it's clear.
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Re: Working together, Wayne and his son can shovel the entire  [#permalink]

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03 Dec 2017, 18:44
cano wrote:
Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel three times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?

A. 4
B. 6
C. 8
D. 9
E. 12

If we let n = the number of hours it takes Wayne to shovel the driveway alone, then 1/n = Wayne’s rate, and 1/(3n) = his son’s rate. Since their combined rate is 1/3, we have:

1/n + 1/(3n) = 1/3

Multiplying by 3n we have:

3 + 1 = n

4 = n

Since Wayne’s son takes three times as long as Wayne to shovel the driveway by himself, it would take him 12 hours to shovel the driveway on his own.

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Re: Working together, Wayne and his son can shovel the entire &nbs [#permalink] 03 Dec 2017, 18:44
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