Q.4 (i) A train travels a distance of 360 km at a uniform speed. If the speed had been 5 km/hr more, the train would have taken 1 hour less for the same journey. Find the speed of the train.
Best answer
Answer: Speed of the train = 40 km/hr
Let the speed be \(x\) km/hr. Time taken \(= \dfrac{360}{x}\) hr; at the higher speed, time \(= \dfrac{360}{x + 5}\) hr.
\(\dfrac{360}{x} - \dfrac{360}{x + 5} = 1\)
\(\dfrac{360(x + 5) - 360x}{x(x + 5)} = 1 \Rightarrow 1800 = x^2 + 5x\)
\(x^2 + 5x - 1800 = 0\)
\(x^2 + 45x - 40x - 1800 = 0 \Rightarrow x(x + 45) - 40(x + 45) = 0 \Rightarrow (x + 45)(x - 40) = 0\)
\(x = -45\) or \(x = 40\). Speed cannot be negative, so \(x = 40\).
Check: \(\dfrac{360}{40} = 9\) hr and \(\dfrac{360}{45} = 8\) hr, a difference of 1 hour.
Log in or create a free account to answer this question.
