A car travels for the first half of the journey's time at 50 km/h and the second half of the time at 70 km/h. What is its average speed?
60 km/h. When the time intervals are equal, the average speed is the simple average of the speeds: (50 + 70)/2 = 60. For example, 1 hour at 50 and 1 hour at 70 covers 120 km in 2 hours.
Explain it simply
This is the twin of the equal-distance question, and it trips people the other way. Here each speed gets the same amount of time, so each speed gets equal weight, and the ordinary average is correct. Read carefully: "half the distance" and "half the time" lead to different formulas.
Example
Question: First half of the time at 50 km/h, second half at 70 km/h. Average speed?
Take total time = 2 hours.
- Distance in hour 1 = 50 km. Distance in hour 2 = 70 km.
- Total = 120 km in 2 hours.
- Average = 60 km/h.
Compare with equal distances at the same two speeds: 2 x 50 x 70 / 120 = 58.33 km/h. Equal time gives a higher average because more distance is covered at the higher speed.
console.log((50 + 70) / 2); // Output: 60
console.log(((2 * 50 * 70) / 120).toFixed(2)); // Output: 58.33What to say in the interview
"With equal time at each speed the speeds carry equal weight, so the average is 60. If the distances were equal instead, I'd use the harmonic mean and get about 58.3."
Common mistakes
- Using the harmonic mean here because it is 'the average speed formula'.
- Not reading whether the halves refer to time or distance.