Question

A man drives 180km from city A to city B in 4 hours 10 minutes and returns to city A in 3 hours 20 minutes. Find the average speed of the whole journey.

Answer 1

Hint:
We will first find the total distance covered in the whole journey and total time taken to cover the journey in hours. Then, divide the total distance covered by total time to calculate the average speed of the journey.

Complete step by step solution:
We are given that the distance between city A and city B is 180km
The man moves to city B from city A and then comes back to city A.
Let us now calculate the total distance travelled by a man by taking twice the distance from city A to city B.
That is, $2\times 180=360km$
Now, we are also given that the time taken by a man from city A to city B is 4 hours 10 minutes and time taken from city B to city A is 3 hours 20 minutes.
The total time taken is the sum of the time taken on both journeys.
Hence, the total time taken is $$\text{4 hours 10 minutes + 3 hours 20 minutes = 7 hours 30 minutes }$$
Now, convert the total time taken in hours, therefore, divide the minutes by 60.
$$\begin{gathered} \text{7 hours 30 minutes = 7 + }{\displaystyle \frac{30}{60}}\text{hours} \\ \Rightarrow \left(\text{7 + 0}\text{.5}\right)\text{hours} \\ \Rightarrow 7.5\text{hours} \end{gathered}$$
As it is known that $\text{speed = }{\displaystyle \frac{\text{distance}}{\text{time}}}$
Therefore, average speed can be calculated by dividing total distance covered by total time taken.
Thus, average speed is ${\displaystyle \frac{360}{7.5}}=48\text{km/hr}$

Hence, the average speed of the journey is 48km/hr.

Note:
Many students do not make the unit the same while putting in the values. Here, we have converted $$\text{7 hours 30 minutes}$$ in hours to substitute the value of time taken. We can convert km/hr to m/s by multiplying the number by ${\displaystyle \frac{5}{18}}$.