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Working together, Wayne and his son can shovel the entire

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cano
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Working together, Wayne and his son can shovel the entire [#permalink] New post   17 Sep 2010, 03:03
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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
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E
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Re: Shovel the driveway [#permalink] New post   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
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Re: Shovel the driveway [#permalink] New post   29 Sep 2010, 04:57
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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
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Re: Shovel the driveway [#permalink] New post   13 Mar 2012, 06:13
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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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Re: Working together, Wayne and his son can shovel the entire [#permalink] New post   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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Re: Working together, Wayne and his son can shovel the entire [#permalink] New post   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] New post   17 Apr 2012, 22:31
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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.

Answer: E.

Hope it's clear.
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Re: Working together, Wayne and his son can shovel the entire [#permalink] New post   03 Dec 2017, 18:44
Expert Reply
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.

Answer: E
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Re: Working together, Wayne and his son can shovel the entire [#permalink] New post   26 Apr 2022, 00:01
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Re: Working together, Wayne and his son can shovel the entire [#permalink]
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