Laura left home at 11:00 hours (11:00 am) and walked along thepath through the forest for eight miles to visit her Aunt who washosting a party. She stopped along the way for lunch, and skippedstones across Lake (the path passes right by Lake), and finallyarrived at Auntâs cottage at 16:00 hours (4:00 pm).
After the party, Laura spent the night at Auntâs and then helpedwith the clean-up the next morning. She left at 11:00 hours (11:00am) to walk home along the same path she had taken the day before(but this time in the reverse direction. This time her feet weresore so she soaked them in the cool creek that ran alongside thepath. Later she stopped to pick berries along the path. She arrivedhome at 16:00 hours (4:00 pm).
a) What was Laura's average rate of travel on each of thedays?
b) Show that:along the path that Laura took through the forest,there is some point that she walked past at exactly the same timeof day on the two days.
Hint: the Intermediate Value Theorem will come in handy
Laura left home at 11:00 hours (11:00 am) and walked along thepath through the forest for eight miles to visit her Aunt who washosting a party. She stopped along the way for lunch, and skippedstones across Lake (the path passes right by Lake), and finallyarrived at Auntâs cottage at 16:00 hours (4:00 pm).
After the party, Laura spent the night at Auntâs and then helpedwith the clean-up the next morning. She left at 11:00 hours (11:00am) to walk home along the same path she had taken the day before(but this time in the reverse direction. This time her feet weresore so she soaked them in the cool creek that ran alongside thepath. Later she stopped to pick berries along the path. She arrivedhome at 16:00 hours (4:00 pm).
a) What was Laura's average rate of travel on each of thedays?
b) Show that:along the path that Laura took through the forest,there is some point that she walked past at exactly the same timeof day on the two days.
Hint: the Intermediate Value Theorem will come in handy
