Answer: B
Let the train travel from the first station to the second at a constant speed of \(x\) km/h. ∴ Time taken to cover 300 km = \(\cfrac{300}{x}\) hours If the train's speed had been 5 km/h more, its speed would be \((x + 5)\) km/h. Then, time taken to cover 300 km = \(\cfrac{300}{x + 5}\) hours ∴ According to the question: \[ \cfrac{300}{x} - \cfrac{300}{x + 5} = 2 \] \[ \cfrac{300(x + 5) - 300x}{x(x + 5)} = 2 \] \[ \cfrac{300x + 1500 - 300x}{x(x + 5)} = 2 \] \[ \cfrac{1500}{x(x + 5)} = 2 \] \[ 2x(x + 5) = 1500 \] \[ x(x + 5) = 750 \] \[ x^2 + 5x - 750 = 0 \] \[ x^2 + 30x - 25x - 750 = 0 \] \[ x(x + 30) - 25(x + 30) = 0 \] \[ (x + 30)(x - 25) = 0 \] ∴ Either \((x + 30) = 0\) or \((x - 25) = 0\) When \((x + 30) = 0\), then \(x = -30\) [But speed cannot be negative] When \((x - 25) = 0\), then \(x = 25\) ∴ The train was traveling at a constant speed of 25 km/h from the first station to the second.
Let the train travel from the first station to the second at a constant speed of \(x\) km/h. ∴ Time taken to cover 300 km = \(\cfrac{300}{x}\) hours If the train's speed had been 5 km/h more, its speed would be \((x + 5)\) km/h. Then, time taken to cover 300 km = \(\cfrac{300}{x + 5}\) hours ∴ According to the question: \[ \cfrac{300}{x} - \cfrac{300}{x + 5} = 2 \] \[ \cfrac{300(x + 5) - 300x}{x(x + 5)} = 2 \] \[ \cfrac{300x + 1500 - 300x}{x(x + 5)} = 2 \] \[ \cfrac{1500}{x(x + 5)} = 2 \] \[ 2x(x + 5) = 1500 \] \[ x(x + 5) = 750 \] \[ x^2 + 5x - 750 = 0 \] \[ x^2 + 30x - 25x - 750 = 0 \] \[ x(x + 30) - 25(x + 30) = 0 \] \[ (x + 30)(x - 25) = 0 \] ∴ Either \((x + 30) = 0\) or \((x - 25) = 0\) When \((x + 30) = 0\), then \(x = -30\) [But speed cannot be negative] When \((x - 25) = 0\), then \(x = 25\) ∴ The train was traveling at a constant speed of 25 km/h from the first station to the second.