Final answer:
It would take them approximately 3.21 hours (or 3 hours and 13 minutes) to build the entertainment center together.
Step-by-step explanation:
To find out how long it would take Jill and Jane to build the entertainment center together, we can use the concept of work rates. Jill can build the entertainment center in 5 hours, so her work rate is 1/5 of the entertainment center per hour. Similarly, Jane can build the entertainment center in 9 hours, so her work rate is 1/9 of the entertainment center per hour.
To find out how long it would take them to build the entertainment center together, we need to add their work rates. The equation is: (1/5 + 1/9) * T = 1, where T represents the time it would take them together. Simplifying this equation, we get: 9/45 + 5/45 = 1/T. Combining like terms, we have: 14/45 = 1/T.
To solve for T, we can take the reciprocal of both sides of the equation. So T = 45/14. This means it would take them approximately 3.21 hours (or 3 hours and 13 minutes) to build the entertainment center together.