# 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.

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’. 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

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