On the same side of a straight river are two towns, and the townspeople want to build a pumping station, See Image. The pumping station is to be at the river's edge with pipes extending straight to the two towns. Where should the pumping station be located to min-
On the same side of a straight river are two towns, and the townspeople want to build a pumping station, See Image. The pumping station is to be at the river's edge with pipes extending straight to the two towns. Where should the pumping station be located to min-
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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Question
On the same side of a straight river are two towns, and
the townspeople want to build a pumping station, See Image.
The pumping station is to be at the river's
edge with pipes extending straight to the two towns.
Where should the pumping station be located to min-
imize the total length of pipe?
Transcribed Image Text:The diagram illustrates the geographic relationship between two towns, labeled as Town 1 and Town 2.
- Town 1 is positioned 1 mile south of a straight line road.
- Town 2 is located 4 miles directly south of the same road.
- The distance between the two towns along the road is marked as "S."
- The road is divided into two segments: one marked as "x" miles, and the total distance between the points of interest on the road is 4 miles.
- The angles shown indicate that a route can be traveled from Town 1 to the road, and then to Town 2.
This diagram is often used to analyze distances for planning routes or studying geographic positioning, particularly in optimizing travel between two points that are not directly aligned.
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