Example

Finding Time Given Distance and Rate

When the total distance and the constant rate of travel are both known, the elapsed time can be found by substituting into d=rtd = rt and solving for tt.

Example: Rey plans to drive from San Diego to Sacramento, a distance of 520520 miles. If he drives at a steady rate of 6565 miles per hour, how many hours will the trip take?

  1. Identify: We need the time (number of hours).
  2. Name: Let tt = time.
  3. Translate: Write d=rtd = rt with d=520d = 520 and r=65r = 65. Substituting gives 520=65t520 = 65t.
  4. Solve: Divide both sides by 6565: t=52065=8t = \frac{520}{65} = 8.
  5. Check: Substitute back into the formula: d=658=520d = 65 \cdot 8 = 520. Because 520=520520 = 520 is true, the solution is confirmed.
  6. Answer: Rey's trip will take 88 hours.

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Updated 2026-04-21

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