Answer :
Answer:
The train traveled for 32.66 hours.
Step-by-step explanation:
Let the speed of the train was initially for [tex]\frac{1}{4}[/tex] the distance was x km/hr.
So, 150 km the train moved with x km/hr speed and the remaining 450 km the train goes with the speed of (x + 15) km/hr.
Then, the time taken by the train to cover the first 150 km will be [tex]\frac{150}{x}[/tex] hrs.
Therefore, with the actual speed, the train would have covered the 150 km by [tex](\frac{150}{x} - 1\frac{1}{2}) = (\frac{150}{x} - \frac{3}{2}) = \frac{300 - 3x}{2x}[/tex] hrs.
Now, from the given conditions, we can write the equation as
[tex]4(\frac{300 - 3x}{2x}) = \frac{150}{x} + \frac{450}{x + 15}[/tex]
⇒ [tex]2(\frac{300 - 3x}{x}) = 150 \times \frac{4x + 15}{x(x + 15)}[/tex]
⇒ (300 - 3x) (x + 15) = 75(4x + 15) {Since x ≠0}
⇒ 300x + 4500 - 3x² - 45x = 300x + 1125
⇒ 3x² + 45x - 3375 = 0
⇒ x² + 15x - 1125 = 0
⇒ [tex]x = \frac{- 15 \pm \sqrt{15^{2} - 4(1)(-1125)}}{2}[/tex] {Applying the quadratic formula}
⇒ x = 26.87 km/hr {Ignoring the negative root}
Therefore, the train traveled for [tex]4(\frac{300 - 3 \times 26.87}{26.87}) = 32.66[/tex] hours. (Answer)
