# What is the average speed?

A train travels at a certain average speed for a distance of 63 km. There after it travels a distance of 72 km with an average speed of 6 km/hr more than the original speed. Total time taken to complete the journey is 3 hours. What is the original average speed of the train?

- 36 km/hr
- 42 km/hr
- 48 km/hr
- None of these

**Answer: (2) 42 km/hr**

**Explanation:-
**Let the original average speed of the train = X km/hr

The distance covered by the train with original average speed = 63 km

Then, the time taken by the train to covered 63 km distance = 63/X hr

If the average speed increased by 6 km/hr and he covered 72 km distance.

Then, the time taken by the train = 72/(X + 6) hr

Total time taken by train = 3 hours

Then, 63/X + 72/(X + 6) = 3

{63 x (X + 6) + 72 X}/X(X + 6) = 3

(63X + 378 + 72 X)/X^{2} + 6X = 3

135X + 378 = 3X^{2} + 18X

3X^{2} + 18X – 135X – 378 = 0

3X^{2} – 117X – 378 = 0

3X^{2} – 126X + 9X – 378 = 0

3X (X – 42) + 9 (X – 42) =

X – 42 = 0

X = 42

Then, the original average speed of the train is 42 km/hr.

Hence, the answer is (2) 42 km/hr.