Number and Algebra

Jeepney fares: a piecewise function you ride every day

Algebra & functions

Pamasahe sa jeep: piecewise function na sinasakyan araw-araw

The fare matrix is a piecewise function; fuel, boundary and passenger counts turn it into a daily break-even problem for the driver.

Where it fits

Piecewise Functions · Term 2 · Week 1
Functions and Their Graphs · Term 1 · Weeks 9–10
Units and Conversion · Term 1 · Weeks 6–9

Competencies

gm11.t2.w1.c1 Illustrate a piecewise function in practical contexts (i.e., fare rates, purchasing, and income tax).
gm11.t2.w1.c2 Solve practical problems involving piecewise functions.
gm11.t1.w10.c2 Apply the functions to model and solve real-life problems.

The data

Traditional jeepney fare matrix (regular fare)
Distance (km)	Regular fare	Discounted fare (20% off)
1–4	₱13.00	₱10.40
5	₱14.80	₱11.84
6	₱16.60	₱13.28
7	₱18.40	₱14.72
8	₱20.20	₱16.16
9	₱22.00	₱17.60
10	₱23.80	₱19.04
15	₱32.80	₱26.24

Regular fare by Distance (km)

Source: Representative 2026 figures for classroom use; check current official rates before using for real decisions. Follows the LTFRB fare-matrix structure: base fare for the first 4 km plus a per-kilometre increment; student, senior and PWD fares are 20% off.

Scenario and worked example

'Bayad po!'

Elicit

Ana rides 7 km to school and 7 km back. The conductor asks for ₱20 each way; she thinks that is too much. Who is right? What should she pay as a student?

Worked example: reading the matrix as a function

Explain

F(d) = \begin{cases} 13 & 0 < d \le 4 \\ 13 + 1.80(d-4) & d > 4 \end{cases}

F(7) = 13 + 1.80(3) = 18.40

\text{Student: } 0.8 \times 18.40 = 14.72

The driver's side

Elaborate

The driver's net income is also a function: fares in, boundary and fuel out.

I(n) = 15n - (900 + 1240)

Graph it

Extend

Plot fare against distance: flat, then a straight line with slope 1.80.
Plot the driver's income against passengers: a line crossing zero at about 143.
Where does each graph 'bend' or cross the axis, and what does that mean?

Discuss in class

Why is the fare function flat for the first 4 km? Who benefits?
If diesel rises by ₱10 per litre, how many more passengers does the driver need?
Modern jeepneys charge a higher base fare. Rewrite the function and compare a 10-km ride.

Problems

5 problems · check your answer, then open the solution

Problem 1 Basic

A jeepney charges ₱13 for the first 4 kilometres and ₱1.80 for every additional kilometre. Find the fare for a 10-kilometre ride.

Your answer (₱)
Show step-by-step solution
1. Additional distance: $10 - 4 = 6$ km.
2. Fare $= 13 + 6 \times 1.80 = 13 + 10.80 = 23.80$ pesos.
Answer: 23.8 ₱
Problem 2 Standard

Students receive a 20% fare discount. What does a student pay for the ₱23.80 ride?

Your answer (₱)
Show step-by-step solution
1. Discount: $0.20 \times 23.80 = 4.76$ .
2. Student fare: $23.80 - 4.76 = 19.04$ pesos (in practice rounded to ₱19).
Answer: 19.04 ₱
Problem 3 Standard

Let $d$ be the distance in kilometres ( $d > 0$ ). Which piecewise function gives the regular fare $F(d)$ in pesos?

Choices a. $F(d) = 13 + 1.80d$ b. $F(d) = \begin{cases} 13 & d \le 4 \\ 13 + 1.80(d-4) & d > 4 \end{cases}$ c. $F(d) = \begin{cases} 13 & d \le 4 \\ 1.80d & d > 4 \end{cases}$ d. $F(d) = 1.80(d-4)$
Show step-by-step solution
1. The fare is flat (₱13) up to 4 km, then increases by ₱1.80 for each kilometre beyond 4.
2. Only choice (b) is constant on $d\le 4$ and adds $1.80(d-4)$ afterwards.
Answer: b
Problem 4 Standard

A jeepney runs 120 km a day and uses 1 litre of diesel per 6 km. Diesel costs ₱62 per litre. Find the daily fuel cost.

Your answer (₱)
Show step-by-step solution
1. Fuel used: $120 \div 6 = 20$ litres.
2. Cost: $20 \times 62 = 1{,}240$ pesos.
Answer: 1240 ₱
Problem 5 Challenge Non-routine

A driver pays a ₱900 daily 'boundary' to the operator and ₱1,240 for fuel. If the average fare collected is ₱15 per passenger, how many passengers are needed just to cover these costs? Round up.

Your answer (passengers)
Show step-by-step solution
1. Daily costs: $900 + 1{,}240 = 2{,}140$ .
2. Passengers needed: $2{,}140 \div 15 = 142.67$ .
3. Round up: 143 passengers before the driver earns anything.
4. Income is the linear function $I(n) = 15n - 2140$ .
Answer: 143 passengers

Graph the fare function More practice: Piecewise Functions More practice: Functions and Their Graphs More practice: Units and Conversion