Dr. Lease leaves his house at exactly 7:20 a.m. every morning. When he averages 45 miles per hour, he arrives at his workplace five minutes late. When he averages 63 miles per hour, he arrives five minutes early. What speed should Dr. Lease average to arrive at his workplace precisely on time?
Let the precise time of arrival =T
45[T + 5/60] =63[T - 5/60], solve for T
T = ½ an hour
Sub the T into the above equation to get one-way distance =26.25 miles
26.25 x 2 =52.50 miles - distance back and forth.
So, to arrive at precise time at the office, he must drive at: 52.5 miles/ 1 hour=52.5 mph - his average speed.