### Work word problems

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,

$$x = \Large \frac{1}{{0.16}} = 6.25 hours$$

6830 x

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

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7712 x

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

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11100 x

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Watch below how to solve this example:

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