Patty and mike are installing new floors in their house. working alone, mike can complete the floor in 10 hours. patty can complete the same floor in 8 hours if working alone. how long will it take them, working together, to finish the floor? round your answer to the nearest hundredth if necessary.
9 hours
0.23 hours
4.44 hours
18 hours

There are several important information's already given in the question. Based on those information's the answer can be easily deduced. 

Time taken by Mike to complete the flooring alone = 10 hours
Time taken by Ratty to complete the flooring alone = 8 hours
Then
Time taken by both of them working together = (10 * 8)/(10 + 8)
                                                                        = 80/18
                                                                        = 4.44 hours
From the above deduction, it can be easily concluded that the correct option among all the options that are given in the question is the third option or the penultimate option.