A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding rag
Model Answer
Let the speed of the train be $x$ km/h.
Time taken at speed $x$ = $\dfrac{480}{x}$ hours
Time taken at speed $(x - 8)$ = $\dfrac{480}{x-8}$ hours
According to the condition:
$$\frac{480}{x-8} - \frac{480}{x} = 3$$
$$480\left(\frac{x - (x-8)}{x(x-8)}\right) = 3$$
$$480 \times 8 = 3x(x-8)$$
$$3840 = 3x^2 - 24x$$
$$x^2 - 8x - 1280 = 0$$
Factorising:
$$x^2 - 40x + 32x - 1280 = 0$$
$$x(x - 40) + 32(x - 40) = 0$$
$$(x + 32)(x - 40) = 0$$
So $x = 40$ or $x = -32$.
Since speed cannot be negative, $x = -32$ is rejected.
∴ The speed of the train is 40 km/h.
Source: Chapter 4, Exercise 4.1 Q2(iv) & Exercise 4.2
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Explanation
- Set up the equation first: use Time = Distance ÷ Speed to write both times, then equate their difference to 3.
- Key step: cross-multiplying gives a standard quadratic; simplify to $x^2 - 8x - 1280 = 0$.
- Factorisation check: find two numbers that multiply to −1280 and add to −8 → those are −40 and +32.
- Reject negative root: speed must be positive, so always state why $x = -32$ is rejected — examiners award a mark for this reasoning.
- Marks are typically split: 1 for forming the equation, 2 for solving it, 1 for rejecting the negative root, 1 for stating the answer.