On a journey of 600 km, a train was delayed 1 hour and 30 min after having covered 1/4 of the way. To arrive on time at the destination, the engine driver had to increase the speed by 15 km/hour. How long did the train travel for?

The train traveled for 32.66 hours.

Step-by-step explanation:

Let the speed of the train was initially for 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 hrs.

Therefore, with the actual speed, the train would have covered the 150 km by hrs.

Now, from the given conditions, we can write the equation as

⇒

⇒ (300 - 3x) (x + 15) = 75(4x + 15) {Since x ≠0}

⇒ 300x + 4500 - 3x² - 45x = 300x + 1125

⇒ 3x² + 45x - 3375 = 0

⇒ x² + 15x - 1125 = 0

⇒ {Applying the quadratic formula}

⇒ x = 26.87 km/hr {Ignoring the negative root}

Therefore, the train traveled for   hours. (Answer)

1^3 + 2^3 + 3^3 +4^3 = (1+2+3+4)^2

step-by-step explanation:

i am only able to answer the first part. i am not sure about the second part. sorry