Word problems
Two-step equation word problems
Solve ten stories involving fixed fees and rates, budgets, halves and consecutive numbers. Choose number wording and print a separate answer key.
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Distance, rate, and time word problems
Model ten pursuit, opposite-direction, and equal-distance travel stories with exact linear equations. Choose digits, number words, or a mixed set and use worked answer keys with exact checks.
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Read the story, identify the requested quantity and show your reasoning. Include the correct unit in your answer.
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Define the unknown, then compare distances
Mark when each traveler starts and how long each one moves. Pursuit stories compare equal distances at catch-up; opposite-direction stories add distances from a simultaneous start; out-and-back stories use the same route distance.
Each key defines x, shows the original equation and isolation, retains the exact fractional result, rounds once to the nearest hundredth, and checks the original distance relationship.
Learning objective
What this activity builds
Define an unknown speed or elapsed time, build a distance relationship, and verify the exact solution before rounding to the nearest hundredth.
Worked example
A driver has a 3-hour head start. A second driver leaves from the same point, travels 60 mph faster, and catches the first after 2 hours. What was the first driver’s speed?
x(3 + 2) = (x + 60)2, so 3x = 120 and x = 40.00 mph.
The first driver travels for five hours while the second travels for two. At catch-up their distances from the shared starting point are equal.
Teaching notes
Make the practice count
- Define x with its unit before writing an equation.
- Mark each departure time and total elapsed time on a timeline.
- Check pursuit and return-trip answers by comparing exact distances.
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