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?

To find the total travel time of the train, we need to calculate the time it took for the train to cover the first 1/4 of the journey and the time it took for the remaining 3/4 of the journey.

First, let's find the distance covered by the train before the delay:
1/4 of the total distance = (1/4) * 600 = 150 km

Now let's find the time it took for the train to cover the first 1/4 of the journey:
We can use the formula: time = distance/speed

Let's assume the initial speed of the train was v km/h. The time taken to cover the first 1/4 of the journey at this speed would be:
150/v hours

Given that the train was delayed by 1 hour and 30 minutes (which is equal to 1.5 hours), the actual time taken to cover the first 1/4 of the journey would be:
150/v + 1.5 hours

To find the speed of the train after the delay, we add 15 km/h to its initial speed:
v + 15 km/h

Now, let's find the time it took for the train to cover the remaining 3/4 of the journey:
3/4 of the total distance = (3/4) * 600 = 450 km

Using the new speed (v + 15 km/h), the time taken to cover the remaining distance would be:
450/(v + 15) hours

To get the total travel time, we add the time taken to cover the first 1/4 of the journey to the time taken to cover the remaining 3/4 of the journey:
Total travel time = (150/v + 1.5) + 450/(v + 15) hours

Now, you can substitute a value for 'v' (the initial speed) to solve for the total travel time of the train.

follow the same method I just showed you in your previous post of a very similar problem.