question_answer

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.

Answer:

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

\[Speed=\frac{Dis\tan ce}{Time}\]

or                     \[Time=\frac{Dis\tan ce}{Speed}\]

Thus, we have

\[3=\frac{75}{x}+\frac{90}{x+10}\]

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

\[\Rightarrow 3(x)(x+10)=75x+750+90x\]

\[\Rightarrow 3{{x}^{2}}+30x=75x+750+90x\]

\[\Rightarrow 3{{x}^{2}}-135x-750=0\]

\[\Rightarrow {{x}^{2}}-45x-250=0\]

\[\Rightarrow {{x}^{2}}-50x+5x-250=0\]

\[\Rightarrow x(x-50)+5(x-50)=0\]

\[\Rightarrow (x+5)(x-50)=0\]

\[\Rightarrow x=-5\] or \[x=50\]

Since, speed cannot be negative

So,                      \[x=50\]

Hence, the initial speed of bus is \[50\text{ }km/hr\].