a fast train takes 3hour less than a slow train for a journey of 600km. if the speed of the slow train is 10km/h less than that of the fast train , find the speed of the two train.
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Let the speed of the slow train be x km/hr. Then the speed of fast train is (x+10) km/hr.
Time taken by the slow train to cover 600 km = 600/x hrs.
Time taken by the fast train to cover 600 km = 600/x+10 hrs.
therefore, 600/x - 600/x+10=3
=> 600(x+10) - 600x/ x(x+10)=3
=>6000/x²=10x
=>3(x²+10x)= 6000
=> x²+ 10x - 2000=0
=>x(x+50)-40(x+50)=0
=>(x+50)(x-40)=0
=> x= -50 or x=40 => x= 40{ since, x cannot be negative}
Hence, the speeds of two trains are 40 km/hr and 50 km/hr.
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