Question

A person drives his car for 3 hours at a speed of 40 km/hr and for 4.5 hours at a speed of 60 km/hr. At the end of it, he finds that he was covered \[\dfrac{3}{5}\]​of the total distance. What is the uniform speed with which he should further drive to cover the remaining distance in 4 hours?
A) 35 km/hr
B) 20 km/hr
C) 65 km/hr
D) 50 km/hr

Answer 1

 Hint: Speed is defined as the distance covered by any object divided by the time taken to cover that distance. Its S.I unit is m/s.
Uniform speed means that the speed is constant throughout the journey.
Where Distance is the total length of the path covered by that object and its unit is metre.
\[Speed = \dfrac{{Distance}}{{Time}}\]
This implies, \[Distance = speed \times Time\]
Speed and distance both are scalar quantities that means they only have magnitude and no direction.

Complete step-by-step answer:
Given, for the time ( \[{t_1}\] ) \[ = 3hrs\] , the man drives at a speed v1 \[ = 40km/hr\]
 Now as we know that,
\[Distance = speed \times Time\]
Then the distance covered till \[{t_1}\] \[ = 40 \times 3 = 120{\text{ }}km\] ( \[{D_1}\] )
Similarly, For the time ( \[{t_2}\] ) \[ = 4.5hrs\] the man drives at a speed v2\[ = 60km/hr\]
Then the distance covered = \[ = {v_2} \times {t_2} = 60 \times 4.5 = 270{\text{ }}km\] ( \[{D_2}\] )
Let us suppose that the total distance that person has to travel be x
Then as per question,
Distance covered till the time = \[\dfrac{3}{5}\]of the total distance
That is,
\[\begin{gathered}
  {D_1} + {D_2} = \dfrac{3}{5}x \\
   \Rightarrow 120km + 270km = \dfrac{3}{5}x \\
\end{gathered} \]
Thus, \[x = 390 \times \dfrac{5}{3} = 650km\]
Hence the total distance that person has to travel = 650 km
And thus the distance remaining = Total distance – Distance covered
\[\begin{gathered}
   \Rightarrow 650km{\text{ }}-{\text{ }}\left( {{D_1}{\text{ }} + {\text{ }}{D_2}} \right){\text{ }} \\
  {\text{ = }}650 - 390 = {\text{ }}260{\text{ }}km \\
\end{gathered} \]
Also we know that, \[Speed = \dfrac{{Distance}}{{Time}}\]
Thus speed at which the man should travel the rest distance for time 4 hrs \[ = \dfrac{{Distance\;remaining}}{{Time\;remaining}} = \dfrac{{260}}{4} = 65km/hr\]

Therefore, clearly we can see that option (C) is the correct answer i.e. the uniform speed with which he should further drive to cover the remaining distance in 4 hours is 65 km/hr.

Note: Always check the unit of all the given data. For example, if distance is given in km and speed is given in m/s then convert both the quantities into the same unit.
\[1{\text{ }}km{\text{ }} = {\text{ }}1000{\text{ }}m\]
\[1km/hr = \dfrac{5}{{18}}m/s\]