SOLUTION: working together,Joseph and Beth can encode a document in 3 hours.Working alone,Beth can do the job 5 hours.How long does it take Joseph to do the job working alone?

Question 177538: working together,Joseph and Beth can encode a document in 3 hours.Working alone,Beth can do the job 5 hours.How long does it take Joseph to do the
job working alone?
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
let x = rate that joseph works at = number of units produced in one hour.
let y = rate that beth works at = number of units produced in one hour.
let 1 = number of units to be produced (the document)
rate * time = number of units produced
working together, beth and joseph can do the job in 3 hours.
(x + y) * 3 = 1
working alone, beth can do the job in 5 hours.
y * 5 = 1
solving for y, we get y = 1/5 = rate that beth works at meaning she can produce 1/5 of the document in one hour.
we can substitute 1/5 for y in the equation:
(x + y) * 3 = 1
that equation becomes:
(x + 1/5) * 3 = 1
remove parentheses to get:
3*x + 3/5 = 1
subtract 3/5 from both sides to get:
3*x = 2/5
divide both sides by 3 to get:
x = 2/15
that is the rate that joseph works at meaning joseph can produce 2/15 of the document in one hour.
let t = the time it takes for joseph to complete the document.
rate * time = units produced
2/15 * t = 1
t = 15/2 = 7.5
it would take joseph 7.5 hours to complete the job.
verify in the original equation:
(x + y) * 3 = 1
substitute 1/5 for y and 2/15 for x to get:
(2/15 + 1/5) * 3 = 1
1/5 is the same as 3/15
equation becomes:
(2/15 + 3/15) * 3 = 1
which becomes
5/15 * 3 = 1
which becomes:
1/3 * 3 = 1
which becomes:
1 = 1
equation is good.
your answer is:
joseph can complete the job in 7.5 hours working alone.

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