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I'm trying to figure out if there's a way to calculate if it's worth taking a toll road if it will save me time.

For example, if the toll only costs 50 cents and my trip will save me 30 minutes, I will take the toll. On the other hand, if the toll is $5 but it will only save me 5 minutes, I will not take the toll.

If feel as if there's a mathematical way to calculate this decision, based on:

  • p = price of the toll
  • t = time saved (estimated)
  • v = value of my time

Sample inputs:

  • p = 2 dollars
  • t = 15 minutes
  • v = $30/hr

Based on this example, is it worth it to take the toll? And how to make this decision for any inputs? Perhaps different inputs are needed? I'm not sure how to set up an equation for this.

splungebob
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1 Answers1

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In general what you want to do is calculate the money per hour for taking the toll or in your notation $p/t$. Then you want to compare that value to the value of your time. If the money per hour calculated is less than the value of your time then it is worth taking, otherwise it is not.

In your case the money per hour for the toll is $p/t=2/(1/4)=8$. So taking the toll costs 8 dollars per hour while you value it at 30 dollars per hour the time you save can be valued at a net 22 dollars per hour.

Chris
  • 472