Final answer:
Andrea and Linda can paint the room together in approximately 8.89 hours.
Step-by-step explanation:
To find out how long it takes for Andrea and Linda to paint the room when they work together, we need to calculate their combined painting rate. Andrea can paint the room in 20 hours, so her painting rate is 1/20 of the room per hour. Linda can paint the room in 16 hours, so her painting rate is 1/16 of the room per hour. When they work together, their combined painting rate is the sum of their rates, which is (1/20 + 1/16) of the room per hour. To calculate how long it takes for them to paint the room, we can take the reciprocal of their combined painting rate. So, it takes them (1/[(1/20) + (1/16)]) hours to paint the room when working together. To simplify the calculation, we can find a common denominator for (1/20) and (1/16), which is 80. Then, the equation becomes (1/[(1/20) + (1/16)]) = (1/[(4/80) + (5/80)]) = (1/[9/80]) = (1 * 80/9) = 80/9 hours. Therefore, it takes Andrea and Linda approximately 8.89 hours (or 8 hours and 53 minutes) to paint the room when they work together.