A minibus takes 6 hour less to cover 1680 km distance, if its speed is increased by 14 kmph ? What is the usual time of the minibus ?

Explanation:-

Let
Usual Speed = X kmph.
Now,
Speed of bus after increasing the speed = (X +14)kmph. -------------- (1)
A ____________1680km ____________B In first case,
Time taken to covered the distance 1680 km = 1680/X ----------- (2)
In Second Case,
Time Taken to covered the distance 1680 km = 1680/(X + 14).
Time difference = 6 Hours.
So,
$$\eqalign{ & \Rightarrow \left[ {\frac{{1680}}{x} - \frac{{1680}}{{\left( {x + 14} \right)}}} \right] = 6 \cr & \Rightarrow 1680\left[ {\frac{{14}}{{\left( {{x^2} + 14x} \right)}}} \right] = 6 \cr & \Rightarrow 280 \times 14 = {x^2} + 14x \cr & \Rightarrow {x^2} + 70x - 56x - 3920 = 0 \cr & \Rightarrow x\left( {x + 70} \right) - 56\left( {x + 70} \right) = 0 \cr & \Rightarrow x = - 70,56. \cr & {\text{hence,}}\,{\text{speed}}\,{\text{of}}\,{\text{minibus}}\,{\text{is}}\,56\,km/h \cr & {\text{put}}\,x = 56\,{\text{in}}\,{\text{equation}}\,(2) \cr & T = \frac{{1680}}{{56}} \cr & \,\,\,\,\,\, = 30\,{\text{hours}} \cr}$$