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

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

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