Question

ok im lost i know its probally simple but please break it down for me.

darla can enter the payroll for xyz company in 12 hours it takes rosie 6 hours to enter the same payroll how long will it take if they worjk together

Answer 1

\[\frac{ 1 }{ \frac{ 1 }{ x }+ \frac{ 1 }{ y }}\]

Answer 2

so we can let x = darla and y = rosie. what we are looking for here is there rate of work, or.. how many jobs can they complete in an hour.

Answer 3

so if darla can do the 1 job in 12 hours.. how many jobs can she do in an hour?

Answer 4

\[\frac{ 1 }{ 12}\] hours... right?

Answer 5

so if darla can do 1/12 jobs per hour.. how many can rosie do?

Answer 6

\[\frac{ 1 }{ 6 }\]

Answer 7

so darla does 1/12 jobs per hour and rosie does 1/6 jobs per hour, when they work together they can complete \[\frac{ 1 }{ 12 }+\frac{ 1 }{ 6 }\] jobs per hour.

Answer 8

\[\frac{ 1 }{ 6 }+\frac{ 1 }{ 12 }=\frac{ 1 }{ 4 }\]

Answer 9

so together, rosie and darla can complete 1/4 jobs per hour.

Answer 10

so the time it takes for them to complete the one job is given by the inverse of 1/12+1/6

Answer 11

wheres does the 1/4 come from

Answer 12

find a common denominator and add right? 2/12 + 1/12 = 3/12 = 1/4

Answer 13

so the inverse of the rate of work is \[\frac{ 1 }{ \frac{ 1 }{ 4 } }\]

Answer 14

do you know how to solve that last division problem?

Answer 15

\[1\div \frac{ 1 }{ 4 } = \frac{ 1 }{ \frac{ 1 }{ 4 } }\times \frac{ 4 }{ 4 }=\frac{ 4 }{ \frac{ 4 }{ 4 } }= \frac{ 4 }{ 1 }=4\]

Answer 16

good luck.

Answer 17

so 4 hours

Answer 18

yes, 4 hours for them to complete the job together.