Question

A car travels \[30\] km at the uniform speed of \[40\] km/hr and next \[30\] km at the speed of \[20\] km/hr. Find its average speed.

Answer 1

Hint: We cannot find the average speed directly. At first, we will find the time taken by the car to cover the distance. Then using the time we will find the average speed.

Complete step-by-step answer:
It is given that a car travels \[30\]km at the uniform speed of \[40\] km/hr and next \[30\] km at the speed of \[20\] km/hr.
We have to find the average speed of the car.
Before finding the average speed, we will find the time taken by the car to cover the given distance.
We know the relation between distance speed and time is given by the formula
\[{\rm{Distance = speed \times time}}{\rm{.}}\]
From this relation the time is being calculated using the following formula,
\[{\rm{time = }}\dfrac{{{\rm{distance}}}}{{{\rm{speed}}}}\] .
So, the time required by the car to cover \[30\]km at the uniform speed of \[40\] km/hr is \[ = \dfrac{{30}}{{40}}\] hours.
Again, the time required to cover the last \[30\] km at the uniform speed of \[20\] km/hr is \[ = \dfrac{{30}}{{20}}\] hours.
So, from the found time we will calculate the total time,
The total time taken by the car is \[ = \dfrac{{30}}{{40}} + \dfrac{{30}}{{20}}\] hours
Let us simplify the above equation so that we get, the required time as \[\dfrac{9}{4}\] hours
Total distance is \[ = 30 + 30 = 60\] km
From the relation \[{\rm{Distance = speed \times time}}{\rm{.}}\] we can say that
\[{\rm{speed = }}\dfrac{{{\rm{distance}}}}{{{\rm{time}}}}\]
But substituting the known values we find the average speed,
The average speed is \[ = \dfrac{{60}}{{\dfrac{9}{4}}}\] km/h
By simplifying the above term we get, the average speed is \[ = 26.67\] km/h
Hence, the average speed of the car is \[ = 26.67\] km/h

Note: We know that distance = speed \[ \times \] time is the primary relation between distance speed and time, which can be rearranged to find one when the other two are given.