ACT Preparation / Unit 9 ACT 0808 worked example, 60 to 90 seconds
Writing a Word Problem as an Equation
The idea
A word problem becomes an equation in four steps. First, read to the question and name what it asks for with a variable, writing down its units. Second, express every other quantity in terms of that variable. Third, find the fact that makes two expressions equal, often a total, a distance formula or a rate, and write the equation. Fourth, solve, then answer the question asked, with units, and check against the story.
In practice
Worked example: two trains leave the same station in opposite directions, one at 60 miles per hour and one at 75. When are they 405 miles apart? Step one: t hours. Step two: the distances are 60t and 75t. Step three: together they total 405, so 60t + 75t = 405. Step four: 135t = 405, so t = 3 hours. Check: 180 + 225 = 405.
Where people slip
The last step is where answers go wrong: a question asking for the faster train's distance wants 225 miles, not t = 3.
Your place on the trail
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Unlocks
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