12. A train takes one hour less to cover 150 km if its speed is increased by 5 km/h. Find its usual speed.
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Answer:
Step-by-step explanation:
Let the usual speed of train be = x km/hr
Thus, the increased speed of the train = (x + 5)km/hr
Time taken by train under usual speed speed to cover 150 km = 150/x
Time taken by train under increased speed to cover 150km = 150(x +5)
Therefore,
= 150/x - 150/(x + 5) = 1
= 150(x+5) - 150x/x(x+5) = 1
= 150x + 750 - 150x / x²+ 5x = 1.
= 750 = x²+ 5x
= x² + 5x - 750 =0
= x² +( -25 - 30)x - 750 = 0
= x² - 25x + 30x - 750 = 0
= x(x - 25) +30 ( x - 25)=0
= (x-25) (x+ 30)
= x= 25 and x= -30
Thus, the usual speed of the train is 25kmph
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