Question

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 10 km /hr more than the first speed .if it takes 3 hrs to complete the total journey find it's first speed

Answer 1

Speed = distance/time

S1 = d1/t1

t1 = d1/S1

t1 = 75/x

t2 = 90/(x+10)  (given)

t1 + t2 = 75/x + 90/(x+10)

3 = 75(x+10)/x(x+10)     + 90x/x(x+10)

3x(x+10) = 75x + 750 + 90x

3x² + 30x = 75x +750 +90x

3x² - 135x -750 = 0

3x² + 15x -150x -750

3x(x+5) - 150(x+5)

(3x - 150)(x+5)

x = 150/3 =50

x = -5

Speed cannot be -ve numbers

So first speed = 50km/hr