A Volvo bus takes half an hour less than a passenger train to travel 118 km between Jalandhar and Pathankot. If the average speed of the Volvo is 10 km/hr more than that of the passenger train, form the quadratic equation to find the average speed of Volvo.

Now let us assume that the speed of the Volvo bus is x km/hr. 

Therefore according to the question speed of the passenger train will be ‘x −10’ km/hr. 

Now we know that the total distance traveled by both trains was 118 km. 

So the time taken by the Volvo bus would be $\frac{118}{\mathrm{x}}$ hr and the time taken by the passenger train would be $\frac{118}{\mathrm{x}-10}$ hr. Now, we also know that the Volvo bus took $\frac{1}{2}$ hr less than the passenger train to travel the whole distance. 

Therefore, we have 

=> $\frac{118}{\mathrm{x}}=\frac{118}{\mathrm{x}-10}+\frac{1}{2}$ 

=> $\frac{118}{\mathrm{x}}-\frac{118}{\mathrm{x}-10}=\frac{1}{2}$ 

=> $\frac{118\mathrm{x}-1180-118\mathrm{x}}{\mathrm{x}(\mathrm{x}-10)}=\frac{1}{2}$ 

=> $2\times -1180={\mathrm{x}}^2-10\mathrm{x}$ 

=> ${\mathrm{x}}^2-10\mathrm{x}+2360=0$ 

Therefore, this is the required equation.