Example

Finding Distance Given Rate and Time

When the rate of travel and the elapsed time are both known, the distance can be found by substituting directly into the formula d=rtd = rt and multiplying.

Example: Jamal rides his bike at a uniform rate of 1212 miles per hour for 3123\frac{1}{2} hours. What distance has he traveled?

  1. Identify: We need the distance traveled.
  2. Name: Let dd = distance.
  3. Translate: Write the formula d=rtd = rt and note that r=12r = 12 mph and t=312t = 3\frac{1}{2} hours. Substituting gives d=12312d = 12 \cdot 3\frac{1}{2}.
  4. Solve: d=1272=42d = 12 \cdot \frac{7}{2} = 42 miles.
  5. Check: At 1212 mph, Jamal covers 1212 miles each hour — so 3636 miles in 33 hours and 4848 miles in 44 hours. Traveling 4242 miles in 3123\frac{1}{2} hours falls between these values, confirming the answer is reasonable.
  6. Answer: Jamal rode 4242 miles.

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Updated 2026-04-21

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