The figure below represents the traffic entering and leaving a type of roundabou

Question

The figure below represents the traffic entering and leaving a type of roundabout road junction in Continental Europe. Such roundabouts ensure the continuous smooth flow of traffic at road junctions. Construct linear equations that describe the flow of traffic along the various branches. (When constructing an equation for each point on the circle, only use the two variables adjacent to that point.) Use these equations to determine the minimum flow possible along x1. What are the other flows at that time? (It is not necessary to compute the reduced echelon form. Use the fact that traffic flow cannot be negative.)

The figure below represents the traffic entering and leaving about" road junction 70 ?? 130 120 12 Such junctions are very common in Europe. Construct a system of equations that describes the flow of traffic along the various branches. (For each point A, B, C, and D, construct an equation involving only the two adjacent variables.) A: B: C: D: What is the minimum flow possible along the branch BC? (Units are vehicles per hour.) vehicles per hour What are the other flows at that time? vehicles per hour vehidles per hour chides per haur ??.

Explanation / Answer

From the given figure we have,

A : x4+130 = x1

B : x1-180 = x2

C : x2+120 = x3

D : x3-70 = x4

Since x2 - (120-70+130-180) = 0 gives x2-0 = 0 ,i.e., x2 = 0

Therefore, minimum flow possible along the branch BC is : x2 = 0 vehicles per hour.

Then, x1 = 180 vehicles per hour

x3 = 120 vehicles per hour

x4 = 50 vehicles per hour.

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