Question 615003: A man travels a total of 4.2 miles each day to and from work. The traveling consumes 72 minutes each day. How many hours would he save in 129 working days if he moved to another residence so that he would travel only 1.7 miles each day, assuming he travels at the same rate?
A)98.3
B)97
C)95.6
D)93.2
E)92.3
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! he travels 4.2 miles each day.
it takes 72 minutes each day.
if he moves to another residence where he only travels 1.7 miles per day, then that would only take 1.7 / 4.2 * 72 minutes = 29.14285714 minutes per day.
he would save 72 - 29.41285714 = 42.85714286 minutes a day.
in 129 days, the number of minutes saved would be equal to 129 * 42.85714286 = 5528.571429 minutes which is equivalent to 92.14285714 hours.
another way to solve this problem is as follows:
he travels 72 minutes a day for 129 days for a total of 9288 minutes which is equivalent to 9288 / 60 = 154.8 hours.
at his new address he would only be traveling 1.7 / 4.2 = .40476619048 = 40.476619048% as long.
at the same rate of travel, he would therefore be traveling a total of .40476619048 * 154.8 = 62.65714286 hours.
subtract 62.65714286 hours from 154.8 hours to get a net savings of 92.14285714 hours.
the number match so the analysis looks good.
another way to look at it is:
he travels 4.2 miles each day and it takes 72 minutes.
his rate of travel is 72 / 4.2 = 17.14285714 minutes per mile.
this is equivalent to 17.14285714 / 60 = .2857142857 hours per mile.
he will save 4.2 - 1.7 = 2.5 miles per day.
at .2857142857 hours per mile, the savings are .7142857143 hours per day * 129 days equals a total savings of 92.14285714 hours.
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