Question

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?

Answer 1

If she works alone, it will take Mary 9 hours to make the costume.

Explanation:

The together rate is the sum of each separate rate.

In this problem:

Together rate: 1/6

Sam's rate: 1/x

Mary is twice as fast as Sam, so her rate is 2/x.

Then

`(1)/(x) + (2)/(x) = (1)/(6)`

`(3)/(x) = (1)/(6)`

`x = 3*6`

`x = 18`

Mary's rate

2/x = 2/18 = 1/9

If she works alone, it will take Mary 9 hours to make the costume.