Question

A train covers a distance of 780 km at $$x$$ km/hr. Had the speed been $$(x - 5)$$ km/hr, the time taken to cover the same distance would have been increased by 1 hour. Write down an equation in $$x$$ and solve it to evaluate $$x$$.

Answer 1

Time taken at speed $$x\text{ km/hr}$$ is $$T_1 = \frac{780}{x}\text{ hours}$$. 

Time taken at speed $$(x - 5)\text{ km/hr}$$ is $$T_2 = \frac{780}{x - 5}\text{ hours}$$. 

Given that the time increases by 1 hour: $$\frac{780}{x - 5} - \frac{780}{x} = 1$$ 

Simplifying the equation: $$780\left(\frac{x - (x - 5)}{x(x - 5)}\right) = 1$$ 

$$\frac{780 \times 5}{x(x - 5)} = 1$$

$$x^2 - 5x = 3900$$

$$x^2 - 5x - 3900 = 0$$ 

Factoring: $$(x - 65)(x + 60) = 0$$

$$x = 65 \quad \text{or} \quad x = -60$$ 

Since speed cannot be negative, reject $$x = -60$$. 

Hence, the equation is $$x^2 - 5x - 3900 = 0$$ and $$x = 65$$.