Q. 234.5( 11 Votes )

# A train travels a

Answer :

Let the average speed of train be x km/h.

Time taken by train to complete first 54 KM = t1 (in hours) Speed after 54 km = (x + 6) km/h

Time taken by train to next 63 km/h = t2 (in hours) Given

t1 + t2 = 3 hours  ⇒54(x +6) + 63 x = 3x(x+6)

⇒54(x +6) + 63 x = 3(x2 + 6x)

⇒54x + 324 + 63x = 3x2 + 18x
⇒117x + 324  = 3x2 + 18x
⇒ 3x2 + 18x - 117x - 324 = 0

⇒3x2 - 99x + 324 = 0

⇒x2 - 33x + 108 = 0

⇒x2 - 36x + 3x - 108 = 0

⇒(x - 36) + 3(x - 36) = 0

⇒x = 36 or x = - 3 [because in this case time(t1) will be negative, which is not possible]

So the average speed of train is 36 km/hr .

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