This is a question on time and distance ?

Let x = fixed amount for the cab

Let y = additional amount per km.

Let z = number of km in the cab

The total cost of a ride is:

f(z) = x + yz

z is variable and x and y are constants, but unknown.

We are told that the 16 km trip costs $156 and the 24 km trip costs $204. Substitute what we know and we have a system of two equations and two unknowns that can be solved:

f(z) = x + yz

156 = x + 16y and 204 = x + 24y

Solving the first equation for x then substituting into the second equation:

156 = x + 16y

156 - 16y = x

204 = x + 24y

204 = 156 - 16y + 24y

48 = 8y

6 = y

Now we can solve for x:

x = 156 - 16y

x = 156 - 16(6)

x = 156 - 96

x = 60

Now the equation is:

f(z) = x + yz

f(z) = 60 + 6z

How much does the 30 km trip cost?  Solve for f(30):

f(30) = 60 + 6(30)

f(30) = 60 + 180

f(30) = $240

The cab charges comprise a fixed charge and the charge of the distance traveled.

cab charges = fixed charge + charge of the distance

f(x) = k₀ + (k₁ * x) → where:

k₀: constant (fixed charge)

k₁: constant

x: number of km

A person paid $156 for a journey of 16 km.

f(x) = k₀ + (k₁ * x) → where: x = 16

f(16) = k₀ + 16.k₁ → where: f(x) = 156

k₀ + 16.k₁ = 156

k₀ = 156 - 16.k₁

Another person paid $204 for the journey of 24 km.

f(x) = k₀ + (k₁ * x) → where: x = 24

f(24) = k₀ + 24.k₁ → where: f(x) = 204

k₀ + 24.k₁ = 204

k₀ = 204 - 24.k₁ → we've seen that: k₀ = 156 - 16.k₁

156 - 16.k₁ = 204 - 24.k₁

- 16.k₁ + 24.k₁ = 204 - 156

8.k₁ = 48

→ k₁ = 6

Recall: k₀ = 156 - 16.k₁

k₀ = 156 - (16 * 6)

→ k₀ = 60

Restart from f(x):

f(x) = k₀ + (k₁ * x) → you substitute by the previous values

f(x) = 60 + 6x → where x is the number of km

The amount paid by a passenger who has traveled 30 km is:

f(x) = 60 + 6x → where x = 30

f(30) = 60 + (6 * 30)

f(30) = $240

The extra 8 km of the second journey cost 204 – 156 = $48

The 16 km mileage part of the first journey was $96

The fixed charge was 156 – 96 = $60

The mileage rate was $6 per mile

A journey of 30km would cost $60 + 30*6 = $240