Question

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?

Answer 1

Answer:

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

$Base\ Charge = \ 20$

$Rate = \ 5$ per mile

Car B

$Base\ Charge = \ 30$

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

$A = Base\ Charge + Rate * m$

$A = 20 + 5 * m$

$A = 20 + 5m$

Set m to 0 to get the initial charge:

$A = 20 + 5*0$

$A=20$

and

$Rate = 5$

Car B:

$B = Base\ Charge + 0 * m$ i.e. Rate is 0

$B = 30+ 0 * m$

$B = 30$

So:

$Initial = 30$ and $Rate = 0$

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

To do this, we set:

$A = B$

$20 + 5m = 30$

$5m = 30- 20$

$5m = 10$

$m = 2$

At 2 miles, their charges will be equal