question_answer

A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours/ find the first speed of the truck.

Answer:

Let the average speed of the truck be \[x\,\,km/hr\].

Then, new average speed of truck \[=(x+20)\,\,km/hr\].

Time taken by truck to cover\[150\,km=\frac{150}{x}hrs\].

and time taken by truck to cover \[200km=\frac{200}{x+20}\,hrs\].

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

\[\frac{150(x+20)+200x}{x(x+20)}=5\]

\[150x+3000+200x=5x(x+20)\]

\[350x+3000=5{{x}^{2}}+100x\]

\[5{{x}^{2}}-250x-3000=0\]

\[{{x}^{2}}-50x-600=0\]

\[{{x}^{2}}-60x+10x-600=0\]

\[x(x-60)+10(x-60)=0\]

\[(x-10)(x-60)=0\]

\[x=-10\] or \[60\]

Since speed cannot be negative.

So,                               \[x=60\]

\[\therefore \] First speed of truck \[=60\text{ }km/hr\].