The concepts needed to solve work problems were thoroughly discussed
in Work Problems: Basic Concepts.
Work Problems: QuickandEasy Estimates discussed estimating techniques which are used on this page.
This lesson gives a detailed solution for the twoperson work problem shown above.
There is also stepbystep guided practice, so you can achieve mastery.
Carol's work rate is one job per 5 hours,
where the ‘job’ is ‘mowing a (particular) lawn’.
Rename this rate so the denominator is ‘1 hour’ instead of ‘5 hours’.
(Remember that dividing by 5 is the same as multiplying by $\frac15$.)
So, Carol does $\frac15$ of the job in $1$ hour.
Now that you've seen how it's done—you definitely don't need to show all this work!
You can just ‘pull the numbers to the front’.
Rename Julia's rate in one easy step:
So, Julia does $\frac13$ of the job in $1$ hour.
Under the Individual Rates Assumption, the combined rate is the sum of the individual rates:
$$ \text{combined rate} \ \ =\ \ \text{sum of individual rates} \ \ =\ \ \overset{\rm Carol's rate}{\overbrace{\frac15\ \frac{\text{job}}{\text{hr}}}} + \overset{\rm Julia's rate}{\overbrace{\frac13\ \frac{\text{job}}{\text{hr}}}} \ \ \overset{\rm add fractions}{\overbrace{=\strut}}\ \ \frac{8}{15}\ \frac{\text{job}}{\text{hr}} $$Working together, they do $\frac{8}{15}$ of the job in $1$ hour.
We want to know how long it takes to do 1 job, working together.
To find this, rename the combined rate so the numerator is 1.
Remember: any number, multiplied by its reciprocal, gives 1.
Together, they can do 1 job in $\frac{15}8$ hours.
Note that $\frac{15}8$ hours is the exact solution.
No decimal approximation has been done up to this point.
Whenever possible, get an exact answer—do any needed approximation at the last step only.
Here, we'll choose to round the answer to one decimal place.
Using your calculator, 15/8 is approximately 1.9 .
Together, Carol and Julia can mow the lawn in about 1.9 hours.
(Note that this agrees with our estimate.)
Back to the top to try another problem!
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.However, you can check to see if your answer is correct. 
PROBLEM TYPES:
