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

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%

Answer - C

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!

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%

Ok, that makes sense too. Thanks Izvos!

Pike and veritias. Liked your approach. Saves a lot of time!!!

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%


Scroll down for the answer

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

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%

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%

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.

The correct answer is C.

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....

Answer will be (C) 40%

Sal's percent of job=(1/5)/(1/3)=3/5=60%
Pat's percent of job=100-60=40%

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%

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.

Answer: C

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)

"S" takes 5 hrs to complete the job

together (S + P) takes 3 hours

Since, In 5 hrs "S" does 100 % work

Therefore, In 3 hrs "S" does 60% work

So, Rest of the work i.e. 40 % should be done by "P"

We need to know the rate of pat

We are given rate of Sal and their rate together.

1/5 + 1/x = 1/3

1/x = 1/3 - 1/5 = 5/15 - 3/15 = 2/15

Pat’s rate = 2/15

If their combined rate is 1/3 then

Pat’s rate/combined rate = 2/15 * 3 = 6/15 = 2/5 = 0.40*100 = 40%

Answer choice C

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