+19 Mr. Earl E. Bird leaves his house for work at exactly 8:00 A.M. every morning. When he averages 40 miles per hour, he arrives at his workplace three minutes late. When he averages 60 miles per hour, he arrives three minutes early. At what average speed, in miles per hour, should Mr. Bird drive to arrive at his workplace precisely on time?
+760 To arrive on time, Mr. Bird needs to find an average speed that falls between the two speeds he already tried. Since he is 3 minutes late at 40 mph and 3 minutes early at 60 mph, we can assume that the correct speed is somewhere in between.
We can use a weighted average to find the correct speed:
Weighted average = (weight of speed A * speed A + weight of speed B * speed B) / (weight of speed A + weight of speed B)
In this case, the weights are the number of minutes Mr. Bird is late or early:
Weight of 40 mph = 3 minutes (late)
Weight of 60 mph = 3 minutes (early)
Plugging in the values, we get:
Weighted average = (3 * 40 + 3 * 60) / (3 + 3)
Weighted average = (120 + 180) / 6
Weighted average = 300 / 6
Weighted average = 50 miles per hour
Therefore, Mr. Bird should drive at an average speed of 50 miles per hour to arrive at his workplace precisely on time.
