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 .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Glimpses of IndiaGlimpses of IndiaGlimpses of India39 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses