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**A model for a single lane of traffic is given by the following pde**

p dv/dx + v dp/dx + dp/dt = 0

Where:

v = kx/p

**Show that**

dp/dt = -k

**Here is my attempt**

v = kx/p

dv/dx = k/p

p= kx/v

dp/dx = k/v

Substituting into original pde:

p (k/p) + v(k/v) + dp/dt=0

Clearly made an error, any help would be great