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# Sal and Pat can finish a job together in 3 hours. If Sal can do the jo

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Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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08 Jul 2011, 19:40
7
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Difficulty:

25% (medium)

Question Stats:

73% (01:23) correct 27% (01:38) wrong based on 424 sessions

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Sal and Pat can finish a job together in 3 hours. If Sal can do the job alone in 5 hours, what percent of the job does Pat do when Sal and Pat finish the entire job together?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%
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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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11 Jul 2011, 04:49
7
5
bschool83 wrote:
Sal and Pat can finish a job together in 3 hours. If Sal can do the job alone in 5 hours, what percent of the job does Pat do when Sal and Pat finish the entire job together?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%

You can also use ratios to get the answer in under 10 secs.

Time taken together : Time taken by Sal = 3:5
Rate of work together : Rate of work of Sal = 5:3
So out of 5, Sal does 3 parts of the job and Pat does 2 parts.
2/5 is 40%.

For more on ratios:
http://www.veritasprep.com/blog/2011/03 ... of-ratios/
http://www.veritasprep.com/blog/2011/03 ... os-in-tsd/
http://www.veritasprep.com/blog/2011/03 ... -problems/
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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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11 Jul 2011, 04:37
5
1
Sal: 1/5 in 1 hour
Sal: 3/5 in 3 hours

Therefore, pat has done 2/5 = 40% of the job.

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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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08 Jul 2011, 20:34
2
Pat can do the Job alone in 1/(1/3 - 1/5) = 1/2/15 hrs = 7.5 hrs

So in 3 hrs, Pat does 3/7.5 * 100 % = 1000/25 = 40%

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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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10 Jul 2011, 22:53
weird, i was getting D (50%)
Subbed in 30 for work done then backsolved and got the same time for Y, therefore 50%.
I didn't understand your method subhashgosh, could you pls explains how you got the first equation.

Thanks!
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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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11 Jul 2011, 01:44
1
subhashghosh wrote:
Pat can do the Job alone in 1/(1/3 - 1/5) = 1/2/15 hrs = 7.5 hrs

So in 3 hrs, Pat does 3/7.5 * 100 % = 1000/25 = 40%

A bit different. I used formula 1/t1+1/t2=1/T

Thus => 1/5 + 1/x (Pet) = 1/3 => 1/5 + 2/15(Pet)= 1/3
=> 2/15 div 1/3 = 40%
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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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11 Jul 2011, 03:58
Ok, that makes sense too. Thanks Izvos!
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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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11 Jul 2011, 04:57
Pike and veritias. Liked your approach. Saves a lot of time!!!
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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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28 Jul 2011, 22:43
Could one of you help me solve this question, based on both Carishma's ratio method and the regular "inverse of time to get the rate" method? I got the answer, but intuitively, and was unable to set up the final equation to determine % contribution to work:

Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a 2nd machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what % of the cartons were sealed by the machine working at the faster rate?
a) 25% b) 33 1/3% c) 50% d) 66 2/3% e) 75%

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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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28 Jul 2011, 23:47
ok worked on it a bit more, if you take the rate of the 2nd machine and divide it by the calculated combined rate, it gives you the % contribution to overall work by that machine:
k/4
3k/8
=2/3 (or 66.66%) or D
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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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21 Aug 2011, 12:05
1
1
pal would take = 3*5/2 = 15/2 hrs to complete the job
OR pal in 1hr can do 2/15 of the job
in 3 hr pal will do 6/15 = 2/5 of the job

2/5 of the job OR 40%
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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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21 Aug 2011, 19:28
1/5 + 1/p = 1/3 => p = 15/2

=> pat can do the work 1 alone in 15/2 hours = > pats rate = 2/15

amount of work done by pat in 3 hours = (2/15)*3 = 2/5

i.e ((2/5)/1)*100 = 40%
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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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02 Feb 2017, 04:08
1) First we need to find Sal's and Pat's rates:
Rate of Sal and Pat working together: $$\frac{1}{3}$$
Rate of Sal: $$\frac{1}{5}$$
Rate of Pat: $$\frac{1}{3}$$-$$\frac{1}{5}=\frac{2}{15}$$
2) Now we can compare rate's of Sal and Pat: $$\frac{1}{5} vs. \frac{2}{15}; \frac{3}{15} vs. \frac{2}{15}$$ While Pat does 2 segments of work, Sal does 3. This means that when the job id done, Pat has completed 40% of work.

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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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02 Feb 2017, 11:39
bschool83 wrote:
Sal and Pat can finish a job together in 3 hours. If Sal can do the job alone in 5 hours, what percent of the job does Pat do when Sal and Pat finish the entire job together?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%

Let the total work be 15 units

(S + P )'s efficiency / hr is 5 units/hr
S's efficiency / hr is 3 units/hr

So, P's efficiency / hr is 2 units/hr

So, P does 2/5*100 => 40% job....

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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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02 Feb 2017, 12:42
bschool83 wrote:
Sal and Pat can finish a job together in 3 hours. If Sal can do the job alone in 5 hours, what percent of the job does Pat do when Sal and Pat finish the entire job together?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%

Sal's percent of job=(1/5)/(1/3)=3/5=60%
Pat's percent of job=100-60=40%
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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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05 Feb 2017, 19:35
Rate of Sal & Pat together = 1\3
Rate of Sal = 1\5
Rate of Pat = 1\3 - 1\5 = 2\15
Total work done by Pat = 2\15 * 3 = 2\5 = 40%
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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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08 Feb 2017, 11:21
bschool83 wrote:
Sal and Pat can finish a job together in 3 hours. If Sal can do the job alone in 5 hours, what percent of the job does Pat do when Sal and Pat finish the entire job together?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%

We are given that Sal and Pat, working together, can complete a job in 3 hours. Since rate = work/time, the combined rate of Sal and Pat is 1/3. We are also given that Sal can complete the job alone is 5 hours; thus he has a rate of 1/5.

Since Sal’s rate + Pat’s rate = the combined rate, Pat’s rate = the combined rate - Sal’s rate. That is, Pat’s rate = 1/3 - 1/5 = 5/15 - 3/15 = 2/15.

Thus, when the job is completed, Pat completes (2/15)(3) = 6/15 = 2/5 = 0.4 = 40% of the job.

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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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26 Mar 2017, 13:04
1) Assume total work = 30 (e.g., cars)

2) Sal:
Work=30 cars
Time alone=5 hours
Speed=30/5=6 cars/hour
Work done in 3 hours (that he works together with Pat)=6*3=18 cars (out of 30 cars)=60%

3) Pat
Work done in 3 hours (that he works together with Sal)=100%-60%=40% (C)
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Re: Sal and Pat can finish a job together in 3 hours. If Sal can do the jo  [#permalink]

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