Functions defined on intervals
Stories about journeys
|
Below are three stories about car rides.
|
Describe each story using functions. Use the Journeys in three parts or the Representing motion at several speeds tools, as well as the Functions on intervals
tool from the general tools list.
|
|
For each story, formulate several interesting questions that
can be answered using one of the representations of the function.
|
|
Answer the questions you posed and note which representation
helped you find the answers.
|
|
|
|
A Ride to the Lake
|
|
Ian and Susan left their house at the same time and headed for the lake in two cars. The distance from their house to the lake is 200 kilometers.
Ian drove at a constant speed of 60 kilometers per hour,
Susan at 80 kilometers per hour. After a quarter of an hour,
Susan realized that she had forgotten to take her swimsuit.
She turned around and returned home. Her mother waited outside
and handed her the swimsuit, and Susan immediately started out
for the lake again.
|
|
|
Motorcycle and Cab
|
The distance from Honeyville to Cape Cake is 410 kilometers.
At 7 am, a cab left Honeyville headed for Cape Cake at
80 kilometers per hour. When it got to Cape Cake,
the cab driver rested, picked up new passengers, and an
hour later drove back to Honeyville.
At 10 am, a motorcycle rider left Cape Cake headed for Honeyville
at 40 kilometers per hour. After 45 minutes the motorcycle
broke down. The biker stopped for two hours
to fix the motorcycle, then continued to Honeyville.
|
|
|
Trip with a Rest
|
|
A bicycle rider left town headed for Gorgeous Falls at a speed
of 16 kilometers per hour. After riding for 3 hours, she stopped
for a one-hour rest, then continued at a speed of 24
kilometers per hour. She reached Gorgeous Falls at the same
time she would have arrived had she ridden the entire
distance at 16 kilometers per hour without stopping along the way.
|
|
|
|
| |
