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lilietta2000

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Can somebody help me with this question please?

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%
 

DentalDeac

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I would say C 40%

I'm not sure if this is the right logic, but Sal can do the job alone in 5 hours. Since they can do it together in 3, Pat is essentially doing 2 hours worth of the work that it would take for Sal to complete alone (out of the 5). So 2/5 is 40%
 

Simiam

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I would say C 40%

I'm not sure if this is the right logic, but Sal can do the job alone in 5 hours. Since they can do it together in 3, Pat is essentially doing 2 hours worth of the work that it would take for Sal to complete alone (out of the 5). So 2/5 is 40%



I got C 40%, but I did it differently.

Sal = 5
Pat = x
Together = 3

AB/A+B

5x/(5+x) = 3
5x = 15 + 3x
x = 7.5

Pat/Sal = 7.5/5 means Sal works 50% faster than Pat.

Pat did 40% of work Sal did 60%
 

ORLO

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The best way to approach this type of problem is to turn it into an actual scenario. Pretend that Sal's job requires him to mow 10 lawns. Since he completes this task in 5 hours, Sal must mow 2 lawns per hour. When Sal and Pat work together, they complete the tasks (mowing 10 lawns) in 3 hours. We already know that Sal mows lawns at a rate of 2 per hour. Since the pair worked for three hours, that would allow Sal to mow 6 lawns. However, since we already assumed that the job entails mowing 10 lawns, Pat must have mowed 4 lawns in that 3 hour time span. Thus, Pat does 40% of the job. (4/10 = 40%).
 

lilietta2000

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I got C 40%, but I did it differently.

Sal = 5
Pat = x
Together = 3

AB/A+B

5x/(5+x) = 3
5x = 15 + 3x
x = 7.5

Pat/Sal = 7.5/5 means Sal works 50% faster than Pat.

Pat did 40% of work Sal did 60%

what do mean by 7.5/5...then sal works 50% faster? Hoe did u get that?
 

Simiam

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Wow I just tried typing out an explanation. It works in my head is basically what it comes down to...
 

DentalDeac

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The best way to approach this type of problem is to turn it into an actual scenario. Pretend that Sal's job requires him to mow 10 lawns. Since he completes this task in 5 hours, Sal must mow 2 lawns per hour. When Sal and Pat work together, they complete the tasks (mowing 10 lawns) in 3 hours. We already know that Sal mows lawns at a rate of 2 per hour. Since the pair worked for three hours, that would allow Sal to mow 6 lawns. However, since we already assumed that the job entails mowing 10 lawns, Pat must have mowed 4 lawns in that 3 hour time span. Thus, Pat does 40% of the job. (4/10 = 40%).

This is the best way to explain it. This is essentially what I did but you did a much better job of explaining it. :thumbup:
 

harrygt

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Can somebody help me with this question please?

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%

Always try to convert it into how much work done per hour.
If Harry can do the entire work in 5 hours, it means he can do 1/5 of the work in each hour.
Now, we know that Harry and Lili do the same work in 3 hours. This means we do 1/3 of the work in an hour. I do 1/5 of the work alone in an hour. I and you do 1/3 of the work in an hour. We should subtract 1/5 from 1/3 to find out how much work Lili does in an hour.

1/3 - 1/5 = 2/15 [work done by Lili in an hour]

Now, to find the percentage of work done by Lili, simply divide 2/15 by 1/3 [done by both] which will give you 2/5 for the final answer.

2/5 = 40%
I hope this will be easier to understand.
 

Streetwolf

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Wow I just tried typing out an explanation. It works in my head is basically what it comes down to...

Pat requires 7.5 hours and Sal 5 hours to do the same job alone. So it takes Pat 7.5/5 = 1.5x the amount of time to do the same job. If they each work on the job together, Pat will be responsible for 1/1.5 ( = 2/3) the amount of the work Sal does.

So this comes out to 40% compared to Sal's 60%. You can see that 40 is 2/3 of 60. It takes Pat 1.5x the time as Sal because Pat is at 2/3 efficiency as Sal.
 

dvduplex

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this is how I did it:

First Step
Sal = 5
Pat = x
Together = 3

Second Steps

AB/A+B = 5x/(5+x) = 3
5x = 15 + 3x
x = 7.5

Third Steps
Pat = 7.5 or (15/2)
Sal = 5 or (10/2)

Fourth Steps
Pat = (2/15) 3 = .40
Sal = (2/10) 3 = .60

Final Steps
Pat= .40 x 100% = 40%, C
 
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