Mathematical Modeling Math Example 4

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Example 4

medium
A car travels at a constant speed vv km/h. Write a model for distance dd after tt hours. If the car must reach a destination 240 km away in 3 hours, what speed is required?

Solution

  1. 1
    Model: d=vtd = vt.
  2. 2
    Set d=240d = 240 and t=3t = 3: 240=v⋅3240 = v \cdot 3, so v=80v = 80 km/h.

Answer

v=80 km/hv = 80 \text{ km/h}
The model d=vtd = vt assumes constant speed (an idealisation). Solving for vv inverts the model to find the required input given a desired output — a common modelling task.

About Mathematical Modeling

The process of using mathematical structures — functions, equations, distributions — to represent, analyze, and predict real-world phenomena.

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