A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed

Solution:

Let the first speed of the truck be x km/h.

$\therefore$ Time taken to cover $150 \mathrm{~km}=\frac{150}{x} \mathrm{~h} \quad$ (Time $\left.=\frac{\text { Distance }}{\text { Speed }}\right)$

New speed of the truck = (x + 20) km/h

$\therefore$ Time taken to cover $200 \mathrm{~km}=\frac{200}{x+20} \mathrm{~h}$

According to the given condition,

Time taken to cover 150 km + Time taken to cover 200 km = 5 h

$\therefore \frac{150}{x}+\frac{200}{x+20}=5$

$\Rightarrow \frac{150 x+3000+200 x}{x(x+20)}=5$

$\Rightarrow 350 x+3000=5\left(x^{2}+20 x\right)$

$\Rightarrow 350 x+3000=5 x^{2}+100 x$

$\Rightarrow 5 x^{2}-250 x-3000=0$

$\Rightarrow x^{2}-50 x-600=0$

$\Rightarrow x^{2}-60 x+10 x-600=0$

$\Rightarrow x(x-60)+10(x-60)=0$

$\Rightarrow(x-60)(x+10)=0$

$\Rightarrow x-60=0$ or $x+10=0$

$\Rightarrow x=60$ or $x=-10$

∴ x = 60                  (Speed cannot be negative)

Hence, the first speed of the truck is 60 km/h.