Question

A car covers four successive 3 km stretches at speeds of 10 km/hr, 20 km/hr, 30 km/hr and 60 km/hr respectively. The average speed of the car for entire journey is
A) 15 km/hr
B) 35 km/hr
C) 20 km/hr
D) 25 km/hr

Answer 1

Hint: For solving this problem, we individually consider all the four cases having different speeds to calculate the individual time. We are given the distance 3 kilometre for each stretch. By using the relationship of speed, evaluate the different times. At last, by taking the ratio of total distance and total time, we easily get the average speed.

Complete step-by-step answer:
Some of the useful formula involved in solving this problem are:
$\begin{align}
  & \text{speed = }\dfrac{\text{distance}}{\text{time}} \\
 & \Rightarrow \text{time = }\dfrac{\text{distance}}{\text{speed}} \\
 & \Rightarrow \text{Average speed = }\dfrac{\text{total distance}}{\text{total time}} \\
\end{align}$
On considering the first stretch,
Distance travelled = 3 km
Speed for the stretch = 10 km/hr
Therefore, time taken = $\dfrac{3}{10}hr$
On considering the second stretch,
Distance travelled = 3 km
Speed for the stretch = 20 km/hr
Therefore, time taken = $\dfrac{3}{20}hr$
On considering the third stretch,
Distance travelled = 3 km
Speed for the stretch = 30 km/hr
Therefore, time taken = $\dfrac{3}{30}hr$
On considering the fourth stretch,
Distance travelled = 3 km
Speed for the stretch = 60 km/hr
Therefore, time taken = $\dfrac{3}{60}hr$
Total time taken:
$\begin{align}
  & \dfrac{3}{10}+\dfrac{3}{20}+\dfrac{3}{30}+\dfrac{3}{60}=\dfrac{3\times 6+3\times 3+3\times 2+3}{60} \\
 & =\dfrac{18+9+6+3}{60} \\
 & =\dfrac{36}{60}hr \\
\end{align}$
So, the total distance involved in the journey is 12 km and the total time taken for the whole journey is $\dfrac{36}{60}hr$.
Therefore, the average speed is:
$\begin{align}
  & \Rightarrow \text{ }\dfrac{\text{total distance}}{\text{total time}}=\dfrac{12}{\dfrac{36}{60}} \\
 & \Rightarrow \dfrac{12\times 60}{36}=\dfrac{12\times 3\times 20}{36} \\
 & \Rightarrow \dfrac{36\times 20}{36}=20km/hr \\
\end{align}$
Therefore, the average speed is 20 km/hr.
Hence, option (C) is correct.

Note: The knowledge of the relationship between speed, distance and time is required for solving this problem. Care must be taken while calculating the total time taken. The LCM should be correct and the corresponding multiplying factor with other numbers should be accommodated. Sometimes students take the average of given speed directly that may give the wrong answer.