Question

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km / hour more, it would have taken 30 minutes less for the journey. Find the original speed of the train.

Answer 1

Time = distance/speed

Given, train covers a distance of 90 km at a uniform speed. Had the speed been 15 km / hour more, it would have taken 30 minutes less for the journey.

Let the usual speed be ‘a’.

\(\frac{90}{a}-\frac{90}{a\,+\,15}=\frac{30}{60}\)

⇒ 90 ×(a + 15 –a) = (a² + 15a)/2

⇒ a² + 15a – 2700 = 0 

⇒ a² + 60a – 45a – 2700 = 0 

⇒ a(a + 60) – 45(a + 60) = 0 

⇒ (a + 60)(a – 45) = 0 

⇒ a = 45 km/hr