A train travels a distance of 3000km at a constant speed. If the speed of the train is increased by 5km an hour , the journey would take 2 hours less.Find the speed of the train.
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let,
the speed of the train= x km/h
we know that,
time = distance/speed
=> time = 300/x
According to the question,
300/x+5 = 300/x - 2/1
=>300/x - 300/x+5 = 2
=>300(x+5)-300(x) = 2
=>300x+1500-300x= 2x²+10x
=>2x² + 10x -1500= 0
=>x² + 5x - 750= 0
=>x= -5±√[(5)² -4(-750)]/2
=>x= -5±√[25 + 3000)]/2
=>x= -5±√3025/2
=>x= -5±55/2
=>x= -5+55/2 and -5-55/2
=>x= 50/2 and -60/2
We have to take positive term,
Since speed is positive..
=>x= 25 km/h
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