Multiple choice

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?

  1. $\displaystyle \frac { 180-x }{ 2 } $
  2. $\displaystyle \frac { x+60 }{ 4 } $
  3. $\displaystyle \frac { 300-x }{ 5 } $
  4. $\displaystyle \frac { 600 }{ 115-x } $
  5. $\displaystyle \frac { 12000 }{ x+200 } $
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Average speed = Total Distance / Total Time. Let total distance be 100. Time 1 = (x) / 40. Time 2 = (100 - x) / 60. Total time = (3x + 200 - 2x) / 120 = (x + 200) / 120. Average speed = 100 / ((x + 200) / 120) = 12000 / (x + 200).

AI explanation

Assume the total distance is 100, making the first part x and the second part (100 - x). The time taken for the first part is x/40 and the time for the second part is (100 - x)/60. Using the average speed formula of total distance divided by total time, we get 100 / (x/40 + (100 - x)/60). Simplifying the denominator gives a common denominator of 120, leading to the fraction 100 / ((3x + 200 - 2x) / 120). This simplifies perfectly to 12000 / (x + 200).

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