**Q) **A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the journey, what was its first average speed?

**Ans: **Let’s consider the first average speed be X km/h

Therefore, time taken to travel 54 km =

Speed in 2nd part (63 km) = X + 6

Therefore, time taken to travel 63 km =

Hence, total time to complete the journey:

= 3

54 (X + 6) + 63 X = 3 X (X + 6)

18 (X + 6) + 21 X = X (X + 6)

X^{2 }– 33 X – 108 = 0

(X – 36) (X + 3) = 0

Since x – 3, therefore x = 36

**Therefore, the first average speed of the train is 36 km/h.**