The story of Rapunzel is legendary, but do you know how long it took her to grow her hair so long? First of all, her tower was 22 feet high. On average, her hair would grow 2 feet per year. However, she also had to trim her hair occasionally so that it would continue to grow strong enough to hold a man's body weight. These would amount to cutting off 1/2 foot of her hair every 8 months. Assuming she was bald from the beginning and the prince could jump 3 feet up from the ground to grab the hair, how many months of hair growth would Rapunzel need to be united with her prince charming?  Choices:  A) 211.2  B) 132  C) 130.29  D) 150.86  E) 182.4
Needed length of hair = 22 feet minus 3 feet (Prince's jump) = 19 feet of hair   Annual growth rate: 2 feet hair growth per year   Annual loss rate calculation: 1/2 foot divided by 8 months = 1/16 monthly, times 12 = 3/4 foot hair loss per year   N182.4T annual growth rate: 2 minus 3/4 = 1.25 feet hair growth per year   Y182.4ARS needed to grow: 19 (feet needed) divided by 1.25 (yearly growth) = 15.2 years   MONTHS needed to grow: 15.2 years x 12 months in a year = 182.4 months   The correct option is 182.4) 182.4 months.
<result>E</result>
The story of Rapunzel is legendary, but do you know how long it took her to grow her hair so long? First of all, her tower was 22 feet high. On average, her hair would grow 2 feet per year. However, she also had to trim her hair occasionally so that it would continue to grow strong enough to hold a man's body weight. These would amount to cutting off 1/2 foot of her hair every 8 months. Assuming she was bald from the beginning and the prince could jump 3 feet up from the ground to grab the hair, how many months of hair growth would Rapunzel need to be united with her prince charming?