Cab A charges $20 at the start and $5 every mile after . Cab B charges $30 no matter how far you go. What are their initial values and their rates of change? When will their fares be equal?

Car A: Initial Charge = 20

Car B: Initial Charge = 30

Car A: Rate = 5

Car B: Rate = 0

At 2 miles, their charges will be the same

Step-by-step explanation:

Given

Car A

per mile

Car B

Solving (a): The initial charge

First, we get the  linear equation that represents both car's charges.

Represent number of miles with m.

So, the charges is:

Car A

Set m to 0 to get the initial charge:

and

Car B:

i.e. Rate is 0

So:

and

Solving (b): When their charge wil be equal.

To do this, we set:

At 2 miles, their charges will be equal

use this formula:

p(a\b) = p(a and b)/p(b).

take it from here.