DAY 56
If you drove to the beach averaging 60 mph and you returned the same distance averaging 40 mph, what would be your average speed?

Answer:

48 miles per hour.......The apparent answer--50 mph--is incorrect. Let's say the distance to the beach is 60 miles--120 miles round trip. (The answer is the same regardless of the distance.) Rate is determined by dividing distance by time. Traveling at 60 mph, it would take 60 minutes. Traveling at 40 mph, it would take 90 minutes. Total driving time is 150 minutes or 2 1/2 hours..... 120 = R(2.5) = 48 mph.

DAY 57
A bottle and a cork cost $1.10. The bottle costs 10 cents more than the cork. What is the cost of each?

Answer:

$.60 for the bottle and $.50 for the cork.........It's easy to say $1.00 for the bottle and $.10 for the cork. But this would be a difference of $.90, which does not satisfy the problem. Trial and error or algebra will give the correct answer [X + (X + 10) = 110], but a more interesting approach is to divide 110 in half--55--and then "split the difference" of 10 cents by going up 5 and down 5---giving 60 and 50.