A train X takes 2 hours less than a train Y to cover a distance of 192 km between two cities. Their average speeds differ by 16 km/hr. How long does the faster train take to cover the journey?

Explanation

Let the faster train take t hours. Its speed is \frac{192}{t}. Slower train speed is \frac{192}{t+2}. Difference is \frac{192}{t} - \frac{192}{t+2} = 16 \implies \frac{12}{t} - \frac{12}{t+2} = 1 \implies t^2 + 2t - 24 = 0. Solving gives positive root t=4.

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