Working together word problems

Together, they can do

1 / 5

+     1 / 20  of the job in 1 minute

1 / 5

+   1 / 20

=   4 / 20

+   1 / 20

=   5 / 20

Now set up a proportion using the following logic.





   1       _____________       x minutes



Cross multiply

5 / 20

×   20 / 5

=   100 / 100 = 1

Together, they can clean all bathrooms in 4 minutes.

Problem #2

Say it is a big house project and Maria could finish the project in 5 days and the husband could do it in 20 days.

How many days will it take husband and wife to finish the work?

It is the exact same problem as problem #1 except that instead of using hours, we are using days.

Therefore, it would take them 4 days to finish.

Problem #3: A complicated working together word problem

It can take Peter 25 days to build a house garage all by himself. If he works with his friend, together they can build the house garage in 20 days

How fast can the friend work alone?

Set up a proportion to find out how much of the work can be done by both of them in 1 day

let x represent the amount of work they can do in 1 day. Notice again how we use 1 to represent the entire job

   1       _____________       20 days

   x       _____________       1 day



Cross multiply

1 × 1 = x × 20

1 = 20x

Divide both sides by 20

1 / 20

=   20 / 20 x

The friend can do   1 / 20

-   1 / 25  of the job in 1 day

The friend can do

5 / 100

-   4 / 100  of the job in 1 day

or    1 / 100

This means that it will take the friend 100 days to finish the house garage by himself

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