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Rational Equations

These problems involve fractional equations which contain variable expressions in the denominators. While many of them are of the proportion form,
students should be aware of any restrictions placed on the variables.
 Related Resources

Interactive resources from our Math Tools project:
Algebra: Rational Equations
The closest match in our Ask Dr. Math archives:
High School: Basic Algebra
NCTM Standards:
Algebra Standard for Grades 912
Access to these problems requires a Membership.

'Ace' Trotter
 Terry Trotter

Algebra, difficulty level 1. A problem from the sports world regarding freethrow percentages.
... more>>

Are You Positive?
 Steve Risberg

Algebra, difficulty level 3. Find all values of x that make a rational expression have a positive value.
... more>>

Blowin' in the Wind
 Steve Weimar Steve Risberg

Algebra, difficulty level 3. A plane flies a roundtrip on a calm day and then flies the same trip
on a windy day. How do the flying times compare?
... more>>

Cherokee Creek Checkers Club
 Terry Trotter

Algebra, difficulty level 1. Until one month ago, the Checkers Club had won 40 of 90 matches so far this year. But last
month they won 3 of every 5 games they played. How many games did
they play last month if their overall winning percentage is now 52%?
... more>>

Examining an Equation
 Steve Risberg

Algebra, difficulty level 2. Find integer solutions to an equation in two variables.
... more>>

Family Fun
 Molly Stanley and Steve Risberg

Algebra, difficulty level 3. The Gonzalez family is competing in a relay race where each family
member runs one lap. How long did it take Vicenta to run hers?
... more>>

Filling the Aquarium
 Terry Trotter

Algebra, difficulty level 2. A workman at a zoo has to clean an aquarium, but forgets to do an important task, thus causing a problem (for us).
... more>>

Fraction Action!
 Steve Risberg

Algebra, difficulty level 2. What happens when you add the denominator to both the numerator and denominator of a fraction?
... more>>

Fraction Debate
 Steve Risberg

Algebra, difficulty level 3. Three students disagree about what happens when you perform a certain operation on a positive proper fraction. Which student do you agree with? Why?
... more>>

Jack and Jill Go Jogging
 Terry Trotter

Algebra, difficulty level 2. Two famous Mother Goose characters take up aerobics, running at some numerical speeds while exercising. How fast can each one jog?
... more>>

The Length of Larry's Rectangle
 Larry Sue

Algebra, difficulty level 2. Larry wants to know the length of his rectangle. Can you help him?
... more>>

Make the Save!
 Steve Risberg

Algebra, difficulty level 1. A hockey goalie has saved 112 out of 131 shots so far this season.
How many consecutive shots does she need to save to raise her save
percentage to .900?
... more>>

Marathon Mitch
 Terry Trotter

Algebra, difficulty level 2. Mitch runs a road race and increases speed twice during the race.
Given his total finishing time, determine his standard running rate.
... more>>

My Bag of Marbles
 Terry Trotter

Algebra, difficulty level 2. Find the probability of drawing a blue marble after additional marbles have been placed in a bag.
... more>>

Painting Partners
 Terry Trotter

Algebra, difficulty level 1. Two house painters combine their skills and talents to make short order of a painting job.
... more>>

Parakeets on Parade
 Terry Trotter

Algebra, difficulty level 2. A flock of parakeets flies a round trip to the feeding ground and
back. Given the total time and distance of the round trip, and the
speed of the wind in each direction, find the flying speed of the
parakeets.
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Pressed for Time
 Steve Risberg

Algebra, difficulty level 2. Due to a late breaking story, a newspaper must use both presses to get
an edition printed in time. Find how long it takes to print a normal
edition using only the newer press.
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Ration Ratios
 Steve Risberg

Algebra, difficulty level 3. Determine the ratio of vegetarian meals to vegetarians at the luncheon.
... more>>

Romance by Rowboat
 Terry Trotter

Algebra, difficulty level 1. Romance on the river motivates a nice upstreamdownstream sort of problem.
... more>>

Take Me Out to the Ballgame
 Annie Fetter

Algebra, difficulty level 4. Determine how many innings a pitcher has thrown as his Earned Run Average changes during a game.
... more>>

The Great Northern Triathlon
 Steve Risberg

Algebra, difficulty level 2. Sven skis, skates, and snowshoes in the winter triathlon. Use the
given information to determine how fast he snowshoes.
... more>>

Tiffany's Triumphs
 Terry Trotter

Algebra, difficulty level 1. Given the number of games that Tiffany has played so far and the number that she has won, how many games would she have to win in a row to get her winning percentage up to 60%?
... more>>

To B or Not To B
 Steve Risberg

Algebra, difficulty level 2. Given a letter pattern, find expressions for the number of B's and the
ratio of B's to total letters in the nth term.
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To Grandmother's House We Go
 Ethel Breuche

Algebra, difficulty level 4. Red Riding Hood goes to visit Grandmother for the holidays at the same time that Grandmother heads out to visit Red. What is the ratio of their speeds?
... more>>

Vexing Variables
 Steve Risberg

Algebra, difficulty level 3. Use two algebraic statements involving three variables to find the
numeric value of the ratio of two of those variables.
... more>>
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