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 total journey, what is its first speed?

Distance = 54 km
Let the average speed be x
Distance = 63 km
The average speed to cover this distance = x + 6
Total time taken = 3 hrs
t = D/S
∴ 54/x + 63/(x+6) = 3
⇒ 54(x+6) + 63x / x(x+6) = 3
⇒ 54x + 324 + 63x = 3x² + 18x
⇒ 3x² - 99x - 324 = 0
⇒ x² - 33x - 108 = 0
⇒ x² - 36x + 3x - 108 = 0
⇒ x(x - 36) + 3(x - 36) = 0
⇒ (x - 36)(x + 3) = 0
Then x = 36 and x = -3
x = -3 is not admissible because it is negative
Then x = 36
So speed = 36 km/hr