Question

A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed . If it takes 3 hours to complete total journey , what is its original average speed ?133007

Answer 1

Let the original speed of the train be x.
For a distance of 63 km, let the speed be x km/h.
So, time = $\frac{63}{x}$
For a distance of 72 km, speed = 6 + x km/h
Time = $\frac{72}{x+6}$
Total time = 3 hours
$$\begin{gathered} \frac{63}{x}+\frac{72}{x+6}=3 \\ \Rightarrow \frac{63x+378+72x}{x\left(x+6\right)}=3 \\ \Rightarrow 63x+378+72x=3x^2+18x \\ \Rightarrow 3x^2-117x-378=0 \\ \Rightarrow \left(3x-126\right)\left(x+3\right)=0 \\ \Rightarrow x=-3,42 \end{gathered}$$

So, the original speed = 42 km/h.