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/h more than the first speed. If it takes 3 hours to complete the total journey, find its first speed.

Let x be the initial speed of the bus we know that

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$
or
$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

Thus, we have

$3=\frac{75}{x}+\frac{90}{x+10}$

$\Rightarrow 3=\frac{75(x+10)+90x}{x(x+10)}$

$\Rightarrow 3\left(x\right)(x+10)=75x+750+90x$

$\Rightarrow 3x^2+30x=75x+750+90x$

$\Rightarrow 3x^2-135x-750=0$

$\Rightarrow x^2-45x-250=0$

$\Rightarrow x^2-50x+5x-250=0$

$\Rightarrow x(x-50)+5(x-50)=0$

$\Rightarrow x=-5orx=50$

Since,speed cannot be negative

So, x=50

Hence,the initial speed of bus is 50 km/hr.