Rational Word Problems

Front

What is an inverse variation?

Back

An inverse variation is a relationship between two variables in which one variable increases as the other decreases, and vice versa. It can be expressed as xy = k, where k is a constant.

Front

If the number of people renting a limo increases, what happens to the cost per person?

Back

The cost per person decreases, demonstrating an inverse relationship.

Front

How do you calculate the combined work rate of two people working together?

Back

Add their individual work rates. If Tim can complete a job in T hours and Tom in M hours, their combined work rate is 1/T + 1/M.

Front

If Tim and Tom can complete a job together in 4 hours, what is their combined work rate?

Back

Their combined work rate is 1/4 of the job per hour.

Front

What is direct variation?

Back

Direct variation is a relationship where one variable is a constant multiple of another, expressed as y = kx, where k is a constant.

Front

If Shawn earns $123 for 20 hours of work, how do you find his hourly wage?

Back

Divide his total pay by the number of hours worked: $123 / 20 hours = $6.15 per hour.

Front

How do you find the total pay for a different number of hours worked in a direct variation scenario?

Back

Use the formula: Total Pay = Hourly Wage x Number of Hours Worked.

Front

If Benny takes 6 hours to clean the attic and Mary takes 12 hours, how do you find their combined time working together?

Back

Calculate their work rates: 1/6 + 1/12 = 1/T, then solve for T.

Front

What is the formula to find the time taken when two people work together?

Back

T = 1 / (1/A + 1/B), where A and B are the times taken by each person individually.

Front

If a job takes 11 hours for one person and 12 hours for another, how do you find the time taken if they work together?

Back

Use the combined work rate formula: 1/11 + 1/12 = 1/T, then solve for T.