It takes a train 45 min to travel from A to B. When the speed of the train is…

Concept: For a fixed distance, speed and time are inversely related — speed = distance ÷ time. So if the same distance is covered at two different speeds (and hence two different times), each speed can be written as distance ÷ (that time), and the difference between the two speeds equals the given speed change.

1. Convert both times to hours: 45 min = 3/4 hr and 48 min = 4/5 hr.

2. Let the distance be x km. Original speed = x ÷ (3/4) = 4x/3 kmph; reduced speed = x ÷ (4/5) = 5x/4 kmph.

3. The speed dropped by 5 kmph, so 4x/3 − 5x/4 = 5.

4. Combine over a common denominator of 12: (16x − 15x)/12 = 5, i.e. x/12 = 5.

5. Solve: x = 60.

Cross-check: at 60 km, the original speed is 4(60)/3 = 80 kmph, giving time 60/80 = 0.75 hr = 45 min; the reduced speed is 5(60)/4 = 75 kmph, giving time 60/75 = 0.8 hr = 48 min. The speeds differ by 80 − 75 = 5 kmph, matching the condition, so the distance is confirmed.