# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-8/11

Exercises: Try Out - Set 8: Real exam simulation to sharpen your skills and build confidence. - Problem 11

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## Exercise 11

### Question

export const metadata = {
  title: "Problem 11",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Ali will depart from city A to city B at <InlineMath math="09.15" /> driving a car with an average speed of <InlineMath math="60" /> km/h. At the same time, Tika heads to city A from city B in her vehicle at a speed of <InlineMath math="70" /> km/h. The distance between city A and city B is <InlineMath math="221" /> km. If they take the same route, they will cross paths at...


### Choices

- [ ] $$10.01$$
- [ ] $$10.20$$
- [ ] $$10.36$$
- [x] $$10.57$$
- [ ] $$11.02$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Problem 11",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Let:
- <InlineMath math="J_A =" /> Distance traveled by Ali until they meet
- <InlineMath math="J_T =" /> Distance traveled by Tika until they meet
- <InlineMath math="v_A =" /> Ali's speed <InlineMath math="= 60" /> km/h
- <InlineMath math="v_T =" /> Tika's speed <InlineMath math="= 70" /> km/h

Since Ali and Tika depart at the same time, the time they take to meet is also the same. Let <InlineMath math="t =" /> time.

Then:

<BlockMath math="\begin{aligned} J_A &= v_A \times t = 60t \\ J_T &= v_T \times t = 70t \end{aligned}" />

Since the total distance is <InlineMath math="221" /> km, then:

<BlockMath math="\begin{aligned} J_A + J_T &= 221 \\ 60t + 70t &= 221 \\ 130t &= 221 \\ t &= 1.7 \text{ hours} \end{aligned}" />

So the time required until they meet is:

<BlockMath math="1.7 \text{ hours} = 1 \text{ hour } 42 \text{ minutes}" />

Thus, they will meet at:

<BlockMath math="09.15 + 1 \text{ hour } 42 \text{ minutes} = 10.57" />


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