- #1

Perplexed553

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## Homework Statement

historical data shows that between 15 and 35 mph, the space x between vehicles (in miles) is x = 0.324/(42.1 - v)

where v is the vehicles speed in miles per hour

Ignoring the length of individual vehicles, what speed will give the tunnel the largest volume in vehicles per hour?

## Homework Equations

x = .324/(42.1-v)

## The Attempt at a Solution

I thought I could set x = 0 (because spacing would be 0 ignoring the length of vehicles) and solve for v. That isn't correct.

They show a solution where Q= cars/hour = (42.1v-v^2) / .324. I don't see where they get this.

Then it looks like they take the derivative with respect to v of the numerator only and set it to next to 0

dQ/dv = 0 = 42.1 -2v/.324 = 21.05 mph. This part makes sense to me but I still don't understand where they get Q = (42.1v - v^2)/.324.