Question

A train covers a distance of 600 km at $$x$$ km/hr. Had the speed been $$(x + 20)$$ km/hr, the time taken to cover the same distance would have been reduced by 5 hours. Write down an equation in $$x$$ and solve it to evaluate $$x$$.

Answer 1

Time taken at speed $$x\text{ km/hr}$$ is $$T_1 = \frac{600}{x}\text{ hours}$$. 

Time taken at speed $$(x + 20)\text{ km/hr}$$ is $$T_2 = \frac{600}{x + 20}\text{ hours}$$. 

According to the problem: $$\frac{600}{x} - \frac{600}{x + 20} = 5$$ 

Simplifying the equation: $$600\left(\frac{x + 20 - x}{x(x + 20)}\right) = 5$$

$$\frac{12000}{x(x + 20)} = 5$$ 

$$x(x + 20) = \frac{12000}{5} = 2400$$

$$x^2 + 20x - 2400 = 0$$ 

Factoring: $$(x + 60)(x - 40) = 0$$

$$x = -60 \quad \text{or} \quad x = 40$$ 

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

Hence, the equation is $$x^2 + 20x - 2400 = 0$$ and the value of $$x = 40$$.