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 Highway left, and then along the road. Car 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. Forest 5Vx +4 +3c – 3x 15 Forest Ranger 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 = 8 miles? (Numerical Answer ONLY) x = 1.5 (b) c = 1/2 miles? Remember that the point must lie between the left end of the highway and the car. (Numerical Answer ONLY) x - 1.5 Think about the case when c is an arbitrary number of miles. Toward what point should the ranger walk in this case?
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 Highway left, and then along the road. Car 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. Forest 5Vx +4 +3c – 3x 15 Forest Ranger 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 = 8 miles? (Numerical Answer ONLY) x = 1.5 (b) c = 1/2 miles? Remember that the point must lie between the left end of the highway and the car. (Numerical Answer ONLY) x - 1.5 Think about the case when c is an arbitrary number of miles. Toward what point should the ranger walk in this case?
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
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Chapter8: Rational Expressions And Equations
Section8.9: Use Direct And Inverse Variation
Problem 503E: The length a spring stretches varies directly with a weight placed at the end of the spring. When...
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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
Highway
left, and then along the road.
Car
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.
Forest
5V x +4 +3c - 3x
Forest
Ranger
T(x) =
15
Toward what point on the road should the ranger walk in order to minimize the travel time to the car if...
(a) c = 8 miles? (Numerical Answer ONLY)
X = 1.5
(b) c = 1/2 miles? Remember that the point must lie between the left end of the highway and the car. (Numerical Answer ONLY)
x 1.5
Think about the case when c is an arbitrary number of miles. Toward what point should the ranger walk in this case?
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