Question

A car travels first 30 km with a uniform speed of $60km{{h}^{-1}}$ and then next 30 km with a uniform speed of $40km{{h}^{-1}}$. Calculate the average speed of the car.
\[\begin{align}
  & A.~~~~~75km{{h}^{-1}} \\
 & B.~~~~~50km{{h}^{-1}} \\
 & C.~~~~~48km{{h}^{-1}} \\
 & D.~~~~~96km{{h}^{-1}} \\
\end{align}\]

Answer 1

Hint: To calculate average speed, first we need to find out the total distance covered by the body and then divide it by total time taken by the body to cover that distance. Here we can calculate the total time of journey by adding time taken for the first 30 km and time taken for the next 30 km.

Complete Step By Step Solution:
If an object travels with uniform speed v for time t and travels distance d. We can say that
$d=vt$
Average speed is the total distance travelled by the body divided by total time taken by the body to cover that distance.
For the first 30 km, the uniform speed is $60km{{h}^{-1}}$ so the time taken will be
$t=\dfrac{d}{v}=\dfrac{30}{60}=\dfrac{1}{2}h$
For the next 30 km, the uniform speed is $40km{{h}^{-1}}$ so the time taken will be
$t=\dfrac{d}{v}=\dfrac{30}{40}=\dfrac{3}{4}h$
So the total distance travelled is
$30+30=60km$
Total time taken is given by sum of time taken for first 30 km and the time taken for next 30 km
$\dfrac{1}{2}+\dfrac{3}{4}=\dfrac{5}{4}=1.25h$
So, the average speed for the total journey will be
\[\dfrac{60}{1.25}=48km{{h}^{-1}}\]
So, the correct option is C.

Note: One must be careful with the units while applying the formulae. Also, be very careful when you add quantities. All of them must be of the same units. The S.I. unit of distance is m and the S.I. unit of time is s, which makes S.I. unit of speed $m{{s}^{-1}}$.