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 ?
A. 15 hours
B. 24 hours
C. 25 hours
D. 30 hours
Answer: Option D
Solution(By Examveda Team)
Let Usual Speed = x kmph. Now, Speed of bus after increasing the speed = (x + 14)kmph. . . . . . . (1) A ____________1680km ____________BIn first case, Time taken to covered the distance 1680 km = $$\frac{{1680}}{x}$$ . . . . . . . (2) In Second Case, Time Taken to covered the distance 1680 km = $$\frac{{1680}}{{x + 14}}$$ Time difference = 6 Hours. So, $$\eqalign{ & \Rightarrow {\frac{{1680}}{x} - \frac{{1680}}{{ {x + 14} }}} = 6 \cr & \Rightarrow 1680 {\frac{{14}}{{ {{x^2} + 14x} }}} = 6 \cr & \Rightarrow 280 \times 14 = {x^2} + 14x \cr & \Rightarrow {x^2} + 70x - 56x - 3920 = 0 \cr & \Rightarrow x\left( {x + 70} \right) - 56\left( {x + 70} \right) = 0 \cr & \Rightarrow x = - 70,56. \cr & {\text{hence,}}\,{\text{speed}}\,{\text{of}}\,{\text{minibus}}\,{\text{is}}\,56\,km/h \cr & {\text{put}}\,x = 56\,{\text{in}}\,{\text{equation}}\,(2) \cr & T = \frac{{1680}}{{56}} \cr & \,\,\,\,\,\, = 30\,{\text{hours}} \cr} $$
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Comments ( 2 )
Related Questions on Speed Time and Distance
A. 48 min.
B. 60 min.
C. 42 min.
D. 62 min.
E. 66 min.
A. 262.4 km
B. 260 km
C. 283.33 km
D. 275 km
E. None of these
A. 4 hours
B. 4 hours 30 min.
C. 4 hours 45 min.
D. 5 hours
Please explain the above rule... I can't understand it
A short Cut formula has been used in the solution.
t and T are two time taken in two difference condition.