DAY 40
A man who drives 2 miles to work must average 30 mph to arrive on time. One morning heavy traffic cut his average speed to 15 mph for the first mile. What speed must he average in the second mile to arrive on time with a 30 mph average for the two miles?

Answer:

The man could not possibly make it to work on time. A trip of 2 miles at an average speed of 30 mph will take 4 minutes. The man averaged 15 mph for the first mile, which means that one mile alone took 4 minutes to drive.

DAY 41
A bicycle climbs a certain hill at 10 mph and returns at 20 mph. What is its average speed for the entire trip? (Credit: James F. Fixx in Solve It!)

Answer:

13 1/3 mph.....The apparent answer---15 mph---is wrong. Speed is determined by dividing distance by time. The answer is the same no matter what the distance.
Assuming the hill is 1 mile, 1 = 10T (going up) and 1 = 20T (going down). 1/10 of 60 = 6 minutes and 1/20 of 60 =3 minutes. So 2 = 9R or R = 2/9. 2/9 of 60 = 13 1/3 mph.