SOLUTION: Chynna can type a report in 5 hours. Bea, who is a slow typist, helped Chynna and together, they finished the report within 3 hours. How long would it take for Bea has she worked a

Question 1011393: Chynna can type a report in 5 hours. Bea, who is a slow typist, helped Chynna and together, they finished the report within 3 hours. How long would it take for Bea has she worked alone.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = quantity of work produced.
quantity of work produced / rate = time it takes to produce the work.
quantity of work / time = how much of the work is being produced per unit of time.

the quantity of work is 1 paper.
the time for chynna is 5 hours.

chynna can type the report in 5 hours.
rate * time = quantity of work becomes rate * 5 = 1
solve for rate to get rate = 1/5
chynna can type 1/5 of the paper each hour that she works.

bea helps chynna and they can finish the report in 3 hours.
when bea helps chynna, their rates are additive.

let x = the rate that bea works at.

rate * time = quantity becomes (1/5 + x) * 3 = 1

distribute the multiplication to get 3/5 + 3x = 1

subtract 3/5 from both sides of the equation to get 3x = 1 - 3/5.

combine like terms to get 3x = 2/5

divide both sides of this equation by 3 to get x = 2/15.

the rate that bea works at is 2/15 of the report for each hour that she works.

if we let x = time it takes bea if she works alone, the rate * time = quantity of work produced equation becomes 2/15 * x = 1

solve for x to get x = 15/2 hours = 7.5 hours.

bea can finish the job herself in 7.5 hours.

for bea, the rate * time = quantity of work produced equation becomes 2/15 * 7.5 = 1 which becomes 15/15 = 1 which becomes 1 = 1.

this confirms the solution is correct.

also confirming would be when bea and chynna work together.

the rate * time equation becomes (1/5 + 2/15) * 3 = 1

since 1/5 = 3/15, this equation becomes (3/15 + 2/15) * 3 = 1 which becomes 5/15 * 3 = 1 which becomes 15/15 = 1 which becomes 1 = 1.

that equation is confirmed to be correct as well when bea's rate is 2/15 of the paper per hour.

answer to your question is that it would take bea 7.5 hours to type the report by herself.

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