Question

solve this ques of quadratic

Answer 1

Let the speed of the train be s

Distance given is 90 kms

∴ Time taken (in hours) = 90 ÷ s (Time = Distance ÷ Speed) ---- ( i )

Now

New Speed = s + 15 (15 km/h more than original speed)

Distance is same = 90 kms

Time taken with this speed = 90 ÷ ( s + 15 )

ATQ

New Time is 30 (1/2 hour) minutes less than time taken earlier

∴ Earlier Time - New time = 1/2

(90 / s) - [ 90 / (s + 15) ] = 1/2

 $\frac{90(s+15)-90s}{s(s+15)} = \frac{1}{2}$

$1350=\frac{s^2+15s}{2}$

s² + 15s - 2700 = 0

s² + 60s - 45 s - 2700 = 0

s( s + 60) - 45 (s + 60) = 0

(s + 60) (s - 45) = 0

∴ s = - 60 which is not possible because speed can not be negative

∴ s = 45

Original speed of train is 45 km/h