A train travels at a certain speed for 30 minutes. After that due to a malfunction, it travels at two-thirds of the original speed and reaches its destination 1 hr 30 mins late. Had the malfunction happened after travelling another 60 km, it would have been only 1 hour late. Find the initial speed of the train.

The train travels at its initial speed for 30 minutes, which is 0.5 hours. The time difference between the two scenarios comes from the train travelling an extra 60 km at its initial speed instead of the reduced speed. The time saved per kilometer is the difference between 1 hour and 1.5 hours late, which is 0.5 hours. Thus, travelling 60 km at the initial speed instead of the reduced speed saves 0.5 hours. Setting up the equation 60 divided by (two-thirds of initial speed) minus 60 divided by initial speed equals 0.5, we get 30 divided by initial speed equals 0.5. Solving this gives the initial speed of the train as 60 kmph.

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