Sam does 1job/5hours. Pat does 1job/phours.

Together, they do it in 3 hours so we get 1/5 + 1/p = 1/3.

1/p = 2/15
p = 15/2 hours.

Percent is part/whole so the part is the 3 hours pat worked on the job, and the whole is the 15/2 hours it takes for him to do the whole job.

3/(15/2) = 3*2/15= 2/5 = 40%

Your mistake was you used p instead of 1/p. then you have to interpret it as a percent.

raleigh wrote:Sam does 1job/5hours. Pat does 1job/phours.

Together, they do it in 3 hours so we get 1/5 + 1/p = 1/3.

1/p = 2/15
p = 15/2 hours.

Percent is part/whole so the part is the 3 hours pat worked on the job, and the whole is the 15/2 hours it takes for him to do the whole job.

3/(15/2) = 3*2/15= 2/5 = 40%

Your mistake was you used p instead of 1/p. then you have to interpret it as a percent.

I made it as 1/p also and I don't think it works. Can you explain how come 3 is the part since 1/3 is their combined rate??

Since you are setting up an equation, the units for both sides must be the same.

Sam's rate + Pat's rate = combined rate
1/5 (job/hour) + 1/p (job/hour) = 1/3 (job/hour)

The second part is that you are looking at hours per job. It takes Pat 15/2 or 7.5 hours to do 1 job. But he worked on this job for 3 hours. The idea of a percent is part/whole. So he did part of what the whole work would be while he was working with Sam. This part was that he worked for 3 hours (they both worked for 3 hours). The whole is it takes him 7.5 hours to complete a whole job. So the percent is 3/7.5 = .4 or 40 percent.

It's just appealing to the definition of percent.

Thanks dude.. Now it's clear.

Great, man. Glad you got it. Sorry I wasn't clear the first time around.

This problem can be solved mentally without any paper/pen.
Here is the easy approach.


S and P together tooks 3 hrs.
S can complete the work in 5 hrs.
So in 1 hr he does 1/5 th of the work.
In 3 hrs he does 3/5 of the work.

Since both complete in 3 hrs,
3/5 +x = 1, x is P's contribution.

so x will 2/5 = 4/10 = 40%

Nicely done.

There are a lot of ways to answer the question

If we know the ratio of their rates we can find the % ( the rate is a constant)

1st way

suppose there are 600 bricks (total job)
S will take 5 hours so s will lay 120 bricks per hour
S and P together lay 200 bricks per hour so P will lay 80 bricks

Hence the % of the job done by P is 40%

2nd way

We know that their rates ratio -------->3:2 hence P will do 40% of the total job

Abdulla 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?

20%
30%
40%
50%
60%

TIME RATIO:
(time for Sal and Pat together) : (time for Sal alone) = (3 hours) : (5 hours) = 3:5.

RATE RATIO:
Time and rate have a RECIPROCAL RELATIONSHIP.
To complete a job in HALF THE TIME, the work must be produced at TWICE THE RATE.
Thus, the rate ratio for Sal and Pat working together versus Sal working alone must be equal to the reciprocal of the value in blue:
(rate for Sal and Pat together) : (rate for Sal alone) = 5:3.

Implication of the ratio in red:
For every 5 units that Sal and Pat produce together, Sal alone produces 3 units, with the result that Pat alone produces the remaining 2 units.
Since Pat produces 2 of every 5 units, Pat's percent of the job = 2/5 = 40%.

The correct answer is C.