Question

Translate into an algebraic expression and simplify if possible. C It would take Maya x minutes to rake the leaves and Carla y minutes, what portion of the leaves do they rake in one minute if they work together?

Answer 1

in one minute they rake
`(y+x)/(xy)` leaves working together.

Explanation:

If Maya rakes the leaves in x minutes, then, in one minute she rakes
`(1)/(x)` leaves.

In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes
`(1)/(y)` leaves.

Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us:
`(1)/(x)+ (1)/(y)`

Now, to simplify this expression:

`(1)/(x)+ (1)/(y) =(y+x)/(xy)`

Thus, in one minute they rake
`(y+x)/(xy)` leaves.