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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» 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 |
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