College Algebra / Unit 7 Alg 395 worked example, 60 to 90 seconds
Solving a Variation Problem
The idea
Solving a variation problem means writing the variation equation from the words, using the given pair to find the constant k, and answering the new case with the completed formula.
In practice
Travel time varies inversely with speed, and a trip takes 4 hours at 60 miles per hour. Write the form: t = k/v. Find k from the given pair: 4 = k/60, so k = 240 — and k has meaning here: 240 is the trip's distance in miles. Answer the new case: at 80 miles per hour, t = 240/80 = 3 hours. The plain-sense audit agrees — faster should mean shorter, and 3 beats 4. Every variation problem is the same three moves: form, constant, answer, with the constant usually naming a real quantity worth pausing on.
Where people slip
Match the form to the words before touching numbers; direct and inverse look alike after k arrives.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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