A bus travels at a certain average speed for a distance of 75 km and then travels a distance of 90 km at an average speed of 10km/h more than the first speed. If it takes 3 hours to complete the total journey, find its first speed.

Let the average speed of bus be x km/h

Time taken by bus to complete first 75 KM = t₁ (in hours)

Speed after 75 km = (x + 10) km/h

Time taken by bus to next 90 km/h = t₂ (in hours)

Given

t₁ + t₂ = 3 hours

75x + 750 + 90x = 3x² + 30x

3x² - 135x - 750 = 0

x² - 45x - 250 = 0

x² - 50x + 5x - 250 = 0

x(x - 50) + 5(x - 50) = 0

x = 50 or x = - 5 [because in this case time(t₁) will be negative, which is not possible]

Average speed of the bus is 50 km/hr.