A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road. The forest ranger can walk 3 miles per hour in the forest and travel 5 miles per hour along the road. In the picture below, the forest ranger walks in a straight line to a point x unit from the end of the road on the left, and then along the road. The total travel time for the ranger to get to the car is the sum of the travel time in the forest and the travel time on the road. Write the total time T as a function of x, using the letter c for the distance from the end of the road on the left to the car. \[ T(x) = \] Toward what point on the road should the ranger walk in order to minimize the travel time to the car if... (a) \( c = 9 \) miles? (Numerical Answer ONLY) \[ x = \] (b) \( c = \frac{1}{5} \) miles? Remember that the point must lie between the left end of the highway and the car. (Numerical Answer ONLY) \[ x = \] Think about the case when c is an arbitrary number of miles. Toward what point should the ranger walk in this case? **Explanation of Diagram:** The diagram shows a "Highway" running horizontally with a "Car" on it. Below the highway is a "Forest," with a "Forest Ranger" standing near trees. A diagonal path marked in blue indicates the ranger's walking path from the forest to the road, with two dimensions labeled: a vertical distance of "2 miles" and a horizontal \( x \) unit distance on the road. The total horizontal distance from the beginning of the road to the car is marked as \( c \) miles.
A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road. The forest ranger can walk 3 miles per hour in the forest and travel 5 miles per hour along the road. In the picture below, the forest ranger walks in a straight line to a point x unit from the end of the road on the left, and then along the road. The total travel time for the ranger to get to the car is the sum of the travel time in the forest and the travel time on the road. Write the total time T as a function of x, using the letter c for the distance from the end of the road on the left to the car. \[ T(x) = \] Toward what point on the road should the ranger walk in order to minimize the travel time to the car if... (a) \( c = 9 \) miles? (Numerical Answer ONLY) \[ x = \] (b) \( c = \frac{1}{5} \) miles? Remember that the point must lie between the left end of the highway and the car. (Numerical Answer ONLY) \[ x = \] Think about the case when c is an arbitrary number of miles. Toward what point should the ranger walk in this case? **Explanation of Diagram:** The diagram shows a "Highway" running horizontally with a "Car" on it. Below the highway is a "Forest," with a "Forest Ranger" standing near trees. A diagonal path marked in blue indicates the ranger's walking path from the forest to the road, with two dimensions labeled: a vertical distance of "2 miles" and a horizontal \( x \) unit distance on the road. The total horizontal distance from the beginning of the road to the car is marked as \( c \) miles.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road. The forest ranger can walk 3 miles per hour in the forest and travel 5 miles per hour along the road. In the picture below, the forest ranger walks in a straight line to a point x unit from the end of the road on the left, and then along the road.
The total travel time for the ranger to get to the car is the sum of the travel time in the forest and the travel time on the road. Write the total time T as a function of x, using the letter c for the distance from the end of the road on the left to the car.
\[ T(x) = \]
Toward what point on the road should the ranger walk in order to minimize the travel time to the car if...
(a) \( c = 9 \) miles? (Numerical Answer ONLY)
\[ x = \]
(b) \( c = \frac{1}{5} \) miles? Remember that the point must lie between the left end of the highway and the car. (Numerical Answer ONLY)
\[ x = \]
Think about the case when c is an arbitrary number of miles. Toward what point should the ranger walk in this case?
**Explanation of Diagram:**
The diagram shows a "Highway" running horizontally with a "Car" on it. Below the highway is a "Forest," with a "Forest Ranger" standing near trees. A diagonal path marked in blue indicates the ranger's walking path from the forest to the road, with two dimensions labeled: a vertical distance of "2 miles" and a horizontal \( x \) unit distance on the road. The total horizontal distance from the beginning of the road to the car is marked as \( c \) miles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91519c15-7bc6-4af2-9e48-ccf1b36c2bf0%2F4e44c05a-6cc7-4dca-8e32-560d97be2fbd%2F54ko202_processed.png&w=3840&q=75)
Transcribed Image Text:A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road. The forest ranger can walk 3 miles per hour in the forest and travel 5 miles per hour along the road. In the picture below, the forest ranger walks in a straight line to a point x unit from the end of the road on the left, and then along the road.
The total travel time for the ranger to get to the car is the sum of the travel time in the forest and the travel time on the road. Write the total time T as a function of x, using the letter c for the distance from the end of the road on the left to the car.
\[ T(x) = \]
Toward what point on the road should the ranger walk in order to minimize the travel time to the car if...
(a) \( c = 9 \) miles? (Numerical Answer ONLY)
\[ x = \]
(b) \( c = \frac{1}{5} \) miles? Remember that the point must lie between the left end of the highway and the car. (Numerical Answer ONLY)
\[ x = \]
Think about the case when c is an arbitrary number of miles. Toward what point should the ranger walk in this case?
**Explanation of Diagram:**
The diagram shows a "Highway" running horizontally with a "Car" on it. Below the highway is a "Forest," with a "Forest Ranger" standing near trees. A diagonal path marked in blue indicates the ranger's walking path from the forest to the road, with two dimensions labeled: a vertical distance of "2 miles" and a horizontal \( x \) unit distance on the road. The total horizontal distance from the beginning of the road to the car is marked as \( c \) miles.
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