# 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?

1. 36 km/hr
2. 42 km/hr
3. 48 km/hr
4. None of these
Monis Rasool Professor Asked on 25th October 2015 in

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)/X2 + 6X = 3
135X + 378 = 3X2 + 18X
3X2 + 18X – 135X – 378 = 0
3X2 – 117X – 378 = 0
3X2 – 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.

Anurag Mishra Professor Answered on 25th October 2015.