Work...1

[nycmathguy]

Is my set up right?

1. Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can finish it in 5 hours. If Paul does the job alone he can finish it in 6 hours. How long will it take for Peter to finish the job alone?

Jane = 1/5

Paul = 1/6

Peter = 1/t

Let t = length of time it will take Peter to finish the job alone.

Total time = 2 hours

1/5 + 1/6 + 1//t = 2

Yes?

2. Jim can dig a hole by himself in 12 hours. John can do it in 8 hours. Jack can do it in 6. How long will it take them if they all work together?

Jim = 1/12

John = 1/8

Jack = 1/6

Let t = length of time for all three to finish the job.

1/12 + 1/8 + 1/6 = 1/x

Yes?

 

[Country Boy]

Perhaps a little picky, but "Jane" is a person, not a number! I would never say "Jane= 1/5".
It would be better to say, "Since Jane paints the fence in 5 hours working alone, she paints at a rate of 1/5 fence per hour".

Yes, when people work together their rates of work add.

 

[nycmathguy]

If Jane paints for 5 hours, then she painted for 5 hours. I don't understand the rate part of the question for each person.

 

[MathLover1]

1.
Jane does the job alone she can finish it in 5 hours: rate 1/5
if Paul does the job alone he can finish it in 6 hours: rate 1/6
Peter: let x represent the time it would take Peter solo, so his rate is 1/x
all together can finish painting the fence in 2 hours: rate 1/2

the sum of individual rates must be equal to rate when all work together

1/5 + 1/6 + 1/x = 1/2

Solving for x

6x + 5x + 30 = 15x |Multiplying thru by 30x so as all denominators = 1
30 = 4x
x = 30/4 or 7.5 hrs,

time it would take Peter solo is 7.5 hrs

note: The formula for “Work” Problems that involve three persons is:

2.
Let t = length of time for all three to finish the job.
Jim = (1/12)t
John = (1/8)t
Jack = (1/6)t

adding all will be equal to 1 (1 job done)

(1/12) t+ (1/8)t + (1/6 )t= 1
(3t)/8= 1
3t= 8
t= 8/3
t=2hours and 40 min

 

[Country Boy]

If Jane paints for 5 hours, then she painted for 5 hours. I don't understand the rate part of the question for each person.

If it takes a person 5 hours to do one job, how much of the job does the person do each hour?

Doing one job in 5 hours is (1 job)/(5 hours)= (1/5) (job/hour) or 1/5 "job per hour'=

 

[nycmathguy]

1.
Jane does the job alone she can finish it in 5 hours: rate 1/5
if Paul does the job alone he can finish it in 6 hours: rate 1/6
Peter: let x represent the time it would take Peter solo, so his rate is 1/x
all together can finish painting the fence in 2 hours: rate 1/2

the sum of individual rates must be equal to rate when all work together

1/5 + 1/6 + 1/x = 1/2

Solving for x

6x + 5x + 30 = 15x |Multiplying thru by 30x so as all denominators = 1
30 = 4x
x = 30/4 or 7.5 hrs,

time it would take Peter solo is 7.5 hrs

note: The formula for “Work” Problems that involve three persons is:

2.
Let t = length of time for all three to finish the job.
Jim = (1/12)t
John = (1/8)t
Jack = (1/6)t

adding all will be equal to 1 (1 job done)

(1/12) t+ (1/8)t + (1/6 )t= 1
(3t)/8= 1
3t= 8
t= 8/3
t=2hours and 40 min

Thank you. Country Boy is now on my ignore list. I can't learn math with someone like him on the team.