Question

# A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. Find the average speed for the first 320 km of the tour.$A.{\text{ }}35.55Km/hr \\ B.{\text{ }}36Km/hr \\ C.{\text{ }}71.11Km/hr \\ D.{\text{ }}77Km/hr \\$

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Hint: Average speed may be defined as the total time taken by the man to cover the total distance. In this question first calculate the total time taken by the man to cover 320 km distance and then divide it by total time.

We know that $\left[ {{\text{time}} = \dfrac{{{\text{distance}}}}{{{\text{speed}}}}} \right]$
Given that the man travels first $160km$ at a speed of $64km/hr$
Time taken to cover $160km$ is
$\Rightarrow {t_1} = \dfrac{{160}}{{64}}hr$
And the next $160km$ travels at a speed of $80km/hr$
Time taken to cover next $160km$ is
$\Rightarrow {t_2} = \dfrac{{160}}{{80}}hr$
Total time taken to cover a distance of $320km$ is given by adding time ${t_1}$ and ${t_2}$
$t = {t_1} + {t_2} \\ t = \left( {\dfrac{{160}}{{64}} + \dfrac{{160}}{{80}}} \right)hr \\ t = \dfrac{9}{2}hr \\$
The average speed is
${\text{avg}}{\text{.speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}} \\ = \dfrac{{320}}{{\dfrac{9}{2}}}km/hr \\ = \dfrac{{640}}{9}km/hr \\ = 71.11km/hr \\$
Hence, the average speed for the first 320 km of the tour is 71.11Km/hr.
So, option C is the correct option.

Note: These types of problems are commonly word problems which tell to find anyone of these distance, time, speed and average speed. In these types of problems remember the relation between speed, distance and time. Read the statement carefully and make the conditions accordingly to solve the problem.