Mike likes to canoe. He can paddle 150 feet per minute. He is planning a river trip that will take him to a destination about 30,000 feet upstream (that is, against the current). The speed of the current will work against the speed that he can paddle.
a. Let be the speed of the current in feet per minute. Write an expression for , the speed at which Mike is moving
relative to the river bank, in terms of .
b. Mike wants to know how long it will take him to travel the 30,000 feet upstream. Write an expression for , the
time in minutes it will take, in terms of .
c. What is the vertical intercept of ? What does this point represent in terms of Mike’s canoe trip?
d. At what value of does the graph have a vertical asymptote? Explain why this makes sense in the situation.
e. For what values of does make sense in the context of the problem?