Mrs. Johnson loved being a science teacher at Willowside Middle School, even if it was all one huge accident.
She used to tell her friends that she did not choose teaching, but rather, teaching chose her. She had always been a great student in all her classes except math. Her English teachers throughout middle and high school raved about her poetry as well as her short stories. They would beg her to send them off for publication and would read them gushingly in class, often with tears in their eyes.
Her high school P.E. teachers would call her parents up each year insisting that she join the track and field team or the volleyball team. Her school, they said, needed her amazing speed and agility to push them over the top and guarantee them the championships. Her mother would nod patiently, always saying that she would talk to her later, but she never did. She knew that her daughter was far more interested in her science fair projects and would pay scant attention to the requirements of a sport team.
The only class that gave Mrs. Johnson any challenge at all was math. She studied carefully, did all her work and generally got good, if not excellent, grades. But deep down she felt insecure about her algebra skills and was quite lost in calculus, which was strange because as much as she would struggle with equations, she was completely able to use them deftly in physics.
Mrs. Johnson graduated from college with a degree in chemistry and every intention to continue on to graduate school. Then she spent a summer working as a summer school teacher in the high school near her university. The experience changed her forever. She found the challenge of explaining chemistry far more interesting that learning about it in school. At the end of the summer the principal approached her with the offer to teach at his suburban school the following year. Impulsively she accepted and 8 years later she was still at Willowside Middle School.
The only real problem that Mrs. Johnson had was her commute. In an idea world, she would rather bike or walk to school. But in actuality, she lived in a city about 40 minutes drive over a small mountain range. She just could not bring herself to move to the Willowside area. So she made the trek early in the morning each weekday and came back late at night. She was starting to question the practicality of this and had secretly done some initial job searches in her area. She wasn’t prepared, though, to let Mr. Strehl, the Willowside principal, know about this. Not yet.
It was on wintery days like this one that Mrs. Johnson really hated the commute. It was dark and the pavement was alternately icy or wet. She drove patiently. There were two signs on the road that always confused her. The first was at the summit. It indicated that the road would be descending at a 6% grade for the next three miles. But after three miles another sign indicated that for the next 4 miles she would be descending at a 4% grade. At the end of those 4 miles, she would enter the Willowside area. She obviously knew that the word “descend” meant “going down” and she vaguely remembered that this could be described as a percent, something like number of feet down for number of feet travelled forward. And while it was true that she had not “liked” math in school, she found it greatly important and useful as an adult. She started to wonder whether she could figure out just how high the mountain range was based on the the road signs and the fact that Willowside was 700 feet above sea level.
Your Task: Is it possible to determine the elevation of the summit? If so, what is it? If not, what is needed?
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