Kevin asked his trainee, Anna, to help call some of his clients to sell a newly-issued municipal bond. If he had to call all of the clients himself, it would take Kevin six hours to complete the job. If Anna alone were to call the clients, it would take her nine hours. Working together, how long will it take Kevin and Anna to call all of the clients?

3.6 hours

Step-by-step explanation:

To solve, create a Rate, Time, Work chart:

Work is rate times time. For Kevin, his work is going to equal x over 6 job. For Anna, her expression for work will equal x over 9 job.

The work is 1 job of calling all clients, so their combined work is equal to 1.  

x over 6 plus x over 9 equals 1

In the rational equation, x is the amount of time it takes Kevin and Anna to call the clients together.  With rational equations, the terms can be added together once they have common denominators.  

x over 6 plus x over 9 equals 1

fraction numerator begin display style x left parenthesis 9 right parenthesis end style over denominator begin display style 6 left parenthesis 9 right parenthesis end style end fraction plus fraction numerator begin display style x left parenthesis 6 right parenthesis end style over denominator begin display style 9 left parenthesis 6 right parenthesis end style end fraction equals fraction numerator begin display style 1 left parenthesis 6 right parenthesis left parenthesis 9 right parenthesis end style over denominator left parenthesis 6 right parenthesis left parenthesis 9 right parenthesis end fraction

fraction numerator 9 x over denominator 54 end fraction plus fraction numerator 6 x over denominator 54 end fraction equals 54 over 54

9 x plus 6 x equals 54

15 x equals 54

x equals 3.6

If Kevin and Anna work together, they can call all the clients in 3.6 hours.

27/4x^6 y^8

step-by-step explanation:

4(3x^2y^4)^3 (2x^3y^5)^4

=

108x^6 y^12 /16x^12 y^20

=

108 /16x^6 y^8

=

27 /4x^6 y^8