Concept explainers
23. Time Required to Go from an Island to a Town An island is 2 miles from the nearest point P on a straight shoreline. A town is 12 miles down the shore from P. See the illustration.
(a) If a person can row a boat at an average speed of 3 miles per hour and the same person can walk 5 miles per hour, build a model that expresses the time T that it takes to go from the island to town as a function of the distance X from P to where the person lands the boat.
(b) What is the domain of Τ?
(c) How long will it take to travel from the island to town if the person lands the boat 4 miles from P?
(d) How long will it take if the person lands the boat 8 miles from Ρ?
To find:
a. To model that expresses the time that it takes to go from the island to the town as a function of distance from .
Answer to Problem 23AYU
Solution:
a.
Explanation of Solution
Given:
1. The shortest distance from the island to shore is 2 miles (Point ).
2. The town is 12 miles from the point .
3. The person can row boat at 3 miles per hour.
4. The person can walk at 5 miles per hour.
Calculation:
The can be expressed as the figure below
Let be the distance from point where person lands in the shore.
Let be the distance the person row the boat.
Let be the distance the person walks.
Let be the average speed of the person when he rows the boat.
Let be the average speed of the person when he walks.
a. Let be the time taken to reach the town form the island.
Where,
To find:
b. To find the domain of .
Answer to Problem 23AYU
Solution:
b.
Explanation of Solution
Given:
1. The shortest distance from the island to shore is 2 miles (Point ).
2. The town is 12 miles from the point .
3. The person can row boat at 3 miles per hour.
4. The person can walk at 5 miles per hour.
Calculation:
The can be expressed as the figure below
Let be the distance from point where person lands in the shore.
Let be the distance the person row the boat.
Let be the distance the person walks.
Let be the average speed of the person when he rows the boat.
Let be the average speed of the person when he walks.
b.
To find:
c. To find time , if the person lands the boat 4 miles from .
Answer to Problem 23AYU
Solution:
c.
Explanation of Solution
Given:
1. The shortest distance from the island to shore is 2 miles (Point ).
2. The town is 12 miles from the point .
3. The person can row boat at 3 miles per hour.
4. The person can walk at 5 miles per hour.
Calculation:
The can be expressed as the figure below
Let be the distance from point where person lands in the shore.
Let be the distance the person row the boat.
Let be the distance the person walks.
Let be the average speed of the person when he rows the boat.
Let be the average speed of the person when he walks.
c. To find time , if the person lands the boat 4 miles from .
To find:
d. To find time , if the person lands the boat 8 miles from .
Answer to Problem 23AYU
Solution:
d.
Explanation of Solution
Given:
1. The shortest distance from the island to shore is 2 miles (Point ).
2. The town is 12 miles from the point .
3. The person can row boat at 3 miles per hour.
4. The person can walk at 5 miles per hour.
Calculation:
The can be expressed as the figure below
Let be the distance from point where person lands in the shore.
Let be the distance the person row the boat.
Let be the distance the person walks.
Let be the average speed of the person when he rows the boat.
Let be the average speed of the person when he walks.
d. To find time , if the person lands the boat 8 miles from .
.
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