Multiple choice

Emily takes a trip, driving with a constant velocity of $90$ $km/h$ to the north except for a $30$ min rest stop. If Emily's average velocity is $75$ $km/h$ to the north, what is the total distance travelled? (in km)

  1. $124$
  2. $225$
  3. $150$
  4. $280$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let d be the total distance. Total time taken = (d / 90) + 0.5 hours. Average velocity = Total distance / Total time, so 75 = d / (d/90 + 0.5). Thus, 75(d/90 + 0.5) = d, which simplifies to (5/6)d + 37.5 = d. Then (1/6)d = 37.5, so d = 225 km.

AI explanation

Let the driving time be t hours; the total time including the 0.5-hour rest stop is t + 0.5 hours. Because average velocity equals total displacement divided by total time, we set 90t / (t + 0.5) = 75. Solving this equation gives 90t = 75t + 37.5, so 15t = 37.5 and t = 2.5 hours. The total distance travelled is the speed multiplied by the driving time, 90 * 2.5, which is 225 km.

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