SOLUTION: An old computer can do the weekly payroll in 5 hours. A newer computer can do the same payroll in 3 hours. The old computer starts on the payroll, and after 1 hour the newer comput

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Question 336093: An old computer can do the weekly payroll in 5 hours. A newer computer can do the same payroll in 3 hours. The old computer starts on the payroll, and after 1 hour the newer computer is brought online to work with the older computer until the job is finished. How long will it take both computers working together to finish the job?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
rate * time = units produced

number of units is 1 weekly payroll.

old computer can do it in 5 hours, so the rate of the old computer is 1/5 of the weekly payroll per hour.

new computer can do it in 3 hours, so the rate of the new computer is 1/3 of the weekly payroll per hour.

these are calculated from the formula of rate * time = units produced.

units produced = 1

old computer formula would be rate * 5 = 1

divide both sides of the equation by 5 to get rate of the old computer = 1/5.

same formula used to get rate of the new computer = 1/3.

for the first hour, the old computer is working alone.

after 1 hour, 1/5 of the job has been done because the rate of the old computer is 1/5 of the weekly payroll per hour.

that leaves 4/5 of the weekly payroll left to be done.

both computers work together to finish the job.

since they are working together, their rates are additive.

the rest of the job is equal to 4/5 of the weekly payroll.

since rate * time = units produced, you get rate * time = 4/5.

since both computers are working together, their rates are additive, so their combined rate is equal to 1/5 + 1/3.

the formula becomes:

(1/5 + 1/3) * time = 4/5

where the combined rate is equal to (1/5 + 1/3).

simplify this equation by combining the fractions of 1/5 and 1/3 by finding the least common denominator and you will get:

(3/15 + 5/15) * time = 4/5

combine these like terms to get:

8/15 * time = 4/5

divide both sides of this equation by 8/15 and you get:

time = (4/5) / (8/15).

this is the same as:

time = (4/5) * (15/8)

simplify this by multiplying it out to get:

time = 60 / 40 = 6/4 = 1.5 hours = 1 and 1/2 hours.

add that to the 1 hour already worked by the old computer and you get a total time of 2 and 1/2 hours.

the question was how long it would take both computers working together to finish the job.

the answer would be 1 and 1/2 hours.