Henry and Irene working together can wash all the windows of...

Henry and Irene working together can wash all the windows of their house in 1 $\mathrm{h} 48 \mathrm{min}$ . Work- ing alone, it takes Henry 1$\frac{1}{2} \mathrm{h}$ more than Irene to do the job. How long does it take each person working alone to wash all the windows?

Key Concepts

Work Rate

A work rate represents the amount of a job that can be completed per unit of time. In these types of problems, rates are typically expressed as a fraction of the work done in one hour or another time unit. This concept is essential because it allows the problem-solver to model how much of the task each individual can complete over a given period.

Combined Work Rates

When multiple people work together on a task, their individual work rates add together to form a combined rate. This means that if one person can complete a certain fraction of the work in an hour and another person can complete another fraction, their joint effort can be modeled by summing these fractions, which is key to setting up the equation to find unknown values.

Algebraic Equation Formation

To solve work rate problems, it is necessary to translate the verbal scenario into algebraic equations. This involves defining variables for the unknown time quantities or rates and using the relationships provided in the problem, such as differences in individual times or the total time taken when working together.

Time Conversion

Many work problems involve mixed time units such as hours and minutes, so converting all time measurements into a consistent unit is crucial. This conversion ensures that the modeled equations are accurate and avoids errors when setting up the rate relationships.

Solving Equations (Including Quadratic Equations)

Once the equations are set up based on the work rate and time relationships, solving for the unknowns may lead to equations that are linear or quadratic in nature. Proficiency in solving these equations, whether by isolating variables or using methods like factoring or the quadratic formula, is essential for finding the individual times for each worker.

Please give Ace some feedback