Sometimes you will encounter a word problem that asks you to determine how long it would take two people working together to finish a job. Solving this type of problem requires a few steps of logic. Let’s jump straight to an example.

**Example:** Jennifer can mop a warehouse in 8.3 hours. Heather can mop the same warehouse in 11.2 hours. Find how long it would take them if they worked together.

**Solution:** We set up an equation to model Jen’s work. We know that Jen can mop a warehouse in 8.3 hours, which means

\(\Large \frac{{1{\text{Warehouse Mopped}}}}{{8.3{\text{ hours}}}} = 0.12{\text{Warehouse Mopped in }}1{\text{ hour}}\)

That is, Jen can mop 12 percent of the warehouse in one hour. We set up a similar equation for Heather. We know that Heather can mop the same warehouse in 11.2 hours, which means

\(\Large \frac{{1{\text{Warehouse Mopped}}}}{{11.2{\text{ hours}}}} = 0.09{\text{Warehouse Mopped in }}1{\text{ hour}}\)

That is, Heather can mop about 9 percent of the warehouse in one hour. Now we can find out how much of the warehouse they can mop *together* in one hour. We have

\(0.12\left( {for Jen} \right) + 0.09\left( {for Heather} \right) = 0.21\)

That is, together they can mop 21 percent of the warehouse in 1 hour. Let’s set up our final equation to model this word problem. We use a simple ratio:

\(\Large \frac{{1{\text{Warehouse Mopped}}}}{{x{\text{ hours}}}} = \Large \frac{{0.21{\text{Warehouse Mopped}}}}{{1{\text{ hour}}}}\)

Cross multiplying gives

\(x = \Large \frac{1}{{0.21}} = 4.76{\text{ hours}}\)

**Another Example:** Molly can clean an attic in 10.6 hours. Jasmine can clean the same attic in 15 hours. If they worked together how long would it take them?

\(\Large \frac{{1 Attic}}{{10.6 hours}} = 0.09 in one hour\)

For Jasmine, we have

\(\Large \frac{{1 Attic}}{{15 hours}} = 0.07 in one hour\)

Together, their labor yields

\(0.09 + 0.07 = 0.16 together in one hour\)

Then we use another ratio to solve the problem

\(\Large \frac{{1 Attic Cleaned}}{{x hours}} = \Large \frac{{0.16 Cleaned}}{{1 hour}}\)

Then, by cross multiplying,

\(x = \Large \frac{1}{{0.16}} = 6.25 hours\)

Below you can **download** some** free** math worksheets and practice.

Solve each question. Round your answer to the nearest hundredth.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**

Solve each question. Round your answer to the nearest hundredth.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**

Solve each question. Round your answer to the nearest hundredth.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**