Working together word problems

We will solve "working together word problems" with proportion. It may easier to tackle than algebra.

Problem #1:

Maria can clean all bathrooms in her house in 5 minutes. Her husband can do the same in 20 minutes. How long will it take them if they work together?

If it takes Maria 5 minutes to do the entire job, then she can do 1/5 of the job in 1 minute.

Similarly, if it takes the husband 20 minutes to do the entire job, then he can do 1/20 of the job in one minute.

Together, the amount of the job they can do in 1 minute is

Together, they can do 5/20 of the job in 1 minute.

Now set up a proportion using the following logic.

If 5/20 of the job can be done in 1 minute, then the entire job or 1 can be done in x minutes.

5/20  _________ 1 minute

1      _________  x minutes

Cross multiply:

Multiplying both sides by 20, we get 5x = 20.

x  = 4 since 5 times 4 equals 20.

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?

Problem #1 and problem #2 are similar working together word problems. The only difference is that instead of using hours, problem #2 is using days. Therefore, it would take them 4 days to finish.

Some working together word problems can be complicated. Problem #3 is a little challenging!

Problem #3:

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.

1  _________ 20 days

x  _________  1 day

Cross multiply

1 × 1 = x × 20

1 = 20x

Divide both sides by 20

The amount of the job Peter can do in 1 day is

The amount of the job the friend can do in 1 day is

The amount of the job the friend can do in 1 day is

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

Working together in sales

Michael Scott, by himself, can close 8 sales in 4 hours. If he works with Dwight, they can close 8 sales in 2 hours. How many hours does it take Dwight to close 8 sales by himself?

For Michael, 8 sales in 4 hours means 2 sales per 1 hour or 2 / 1

Michael's sales / hour + Dwight's sales / hour =  together's sales per hour

Dwight's sales / hour is x / 1

Together, 8 sales in 2 hours means 4 sales per 1 hour or 4 / 1

2 / 1 + x / 1 = 4 / 1

2 + x = 4

2 - 2 + x = 4 - 2

x = 2

So Dwight can do 2 sales per hour. It is basically the same as Michael. In this case, he can also do 8 sales in 4 hours.

Want more working together word problems?