Mary can make a costume twice as fast as Sam can. If they both work together, they can make it in 6 hours. How long will it take Mary to make the costume if she works alone?

9 hours

Step-by-step explanation:

Assume the following :

Sam's rate = y for the costume

Mary is twice as fast as Sam; therefore,

Mary's rate = 2y for the costume

If Sam and Mary both work together, it will take them 6hours to make the costume.

Their rate = 1/6

That is,

y + 2y = 1/6

3y = 1/6

18y = 1

y = 1/18 ; taking reciprocal to get time taken = 18 hours

2y = 2/18

2y = 1/9 (9 hours (reciprocal)) timetaken by Mary.

Time taken by Sam = 18 hours

Time taken by Mary = 9 hours