1.

A train travels a distance of 300km constant speed. If the speed of the train is increased by 5 km, the journey would have taken 2 hours less. Find the original speed of the train

Answer»

Let x km/hr be the speed.

Let the time required to travel in the same speed be \(\frac{300}{x}\) hour. 

If the speed is increased by 5 km/ hr the time will decreased by 2 hours.

\(\frac{300}{x}-2=\frac{300}{x+5}\)

\(\frac{300-2x}{x}=\frac{300}{x+5}\)

-2x2 + 290x + 1500 = 300x

x2 + 5x - 720 = 0

\(x=\frac{-5\pm \sqrt{25+3000}}{2}=\frac{-5\pm55}{2}=25,-30\)

Speed will not be negative, therefore x = 25

Speed = 25 km/hour



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