Algebra II : Direct Proportionality

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #21 : Basic Single Variable Algebra

Suppose a runner's distance is directly proportional to her time.  If the runner completes 6 miles in 70 minutes, how many minutes did it take the runner to run 4 miles?

Possible Answers:

Correct answer:

Explanation:

Write the equation for direct proportionality.

Substitute the distance and time to solve for the  constant.

Divide by 70 on both sides.

Substitute this value back to .

The equation becomes:

Substitute  to determine how long it took the runner to run 4 miles.

Multiply by  on both sides to isolate the time variable.

Simplify both sides.

The answer is:  

Example Question #22 : Direct Proportionality

The distance of a cyclist is directly proportional to the time he has traveled. Suppose he has traveled 12 miles in 1.5 hours. How far does he travel in a half hour?

Possible Answers:

Correct answer:

Explanation:

Write the equation for direct proportionality.

Substitute the distance and time given to solve for the constant of proportionality, .

Divide by 1.5 on both sides.

Write the equation.

Substitute half an hour for the time to determine the distance the biker has traveled.

The biker traveled four miles in a half hour.

The answer is:  

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