Mr. Earl E. Bird leaves his house for work at exactly 8:00 AM 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?

Question

anonymous · Answer

50mph

anonymous · Answer

How did you get that? @iTrinity

anonymous · Answer

cause it's halfway between 40 and 60.

anonymous · Answer

and he was either 3 minutes early (60) 0 minutes early (50) or 3 minutes late (40)

anonymous · Answer

Let t be the elapsed time, "on time", in hours and d be travel distance.
Solve the following equations for t and d, $$\left\{t+\frac{3}{60}=\frac{d}{40},t-\frac{3}{60}=\frac{d}{60}\right\} $$$$\left\{t=\frac{1}{4},d=12\right\} $$

anonymous · Answer

$$r=\frac{d}{t}=\frac{12}{\frac{1}{4}}=48 \text{mph} $$