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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?

Sagot :

MrRoyal

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

[tex]Base\ Charge = \$20[/tex]

[tex]Rate = \$5[/tex] per mile

Car B

[tex]Base\ Charge = \$30[/tex]

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

[tex]A = Base\ Charge + Rate * m[/tex]

[tex]A = 20 + 5 * m[/tex]

[tex]A = 20 + 5m[/tex]

Set m to 0 to get the initial charge:

[tex]A = 20 + 5*0[/tex]

[tex]A=20[/tex]

and

[tex]Rate = 5[/tex]

Car B:

[tex]B = Base\ Charge + 0 * m[/tex] i.e. Rate is 0

[tex]B = 30+ 0 * m[/tex]

[tex]B = 30[/tex]

So:

[tex]Initial = 30[/tex] and [tex]Rate = 0[/tex]

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

To do this, we set:

[tex]A = B[/tex]

[tex]20 + 5m = 30[/tex]

[tex]5m = 30- 20[/tex]

[tex]5m = 10[/tex]

[tex]m = 2[/tex]

At 2 miles, their charges will be equal

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