WAEC 2015 Mathematics · Question 5
The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4…
Question
The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 litres of petrol is consumed on a distance of 15km. how far would the vehicle go on 9 litres of petrol?
- A.22km
- B.30km
- C.33km
- D.45km
Answer: A. 22km
Explanation written with AI and checked against the answer key
Analyze the question Petrol consumed (P) varies directly as the square of the distance (d). This is direct variation with a square. Concept P ∝ d², so P = kd², where k is a constant. Solution Step 1: Find k using P = 4 when d = 15. 4 = k(15²) = 225k k = 4/225 Step 2: Find d when P = 9. 9 = (4/225)d² d² = (9 × 225)/4 = 2025/4 d = √2025 / √4 = 45/2 = 22½ km Answer: A (22½ km) Quick check: Petrol went from 4 to 9 litres, a ratio of 9/4. Since P ∝ d², the distance ratio is √(9/4) = 3/2. So the new distance is 15 × 3/2 = 22.5 km. ✔ Tip: In "varies as the square" questions, use the ratio method: P₁/P₂ = d₁²/d₂². Then take the square root of the ratio to get the distance ratio, which saves time in the exam. Don't be tempted by option D (45 km), which comes from forgetting to divide by 2 after the square root.AI can make mistakes. Report anything that looks wrong.
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