Question

A man walks at a speed of 6km/hr for 1km and 8km/hr for the next 1km. What is his average speed for the walk of 2km?

Answer 1

Average speed is the total distance traveled divided by total time taken to cover that distance.

Complete step by step answer:
The average speed is defined as the total distance covered per unit total time taken. Here a man walks at a speed of 6 kilometers per hour for the first kilometer, and then walks at a speed of 8 kilometers per hour for the next kilometer. We must find out the average speed for his total walk.
For calculating the average speed, we need to know the total distance covered by him. Since this is already mentioned in the question, we know the total distance covered by him is 2 kilometers.
Now we must calculate the total time taken by him to cover that distance. We know that for the first kilometer, he walks at a speed of 6 kilometers per hour. Therefore, we could calculate the time taken by him for the first kilometer
${v_1} = 6km/hr,{d_1} = 1km$
speed\left( v \right) = \dfrac{{dis\tan ce\left( d \right)}}{{time\left( t \right)}} \\\ \therefore {t_1} = \dfrac{{{d_1}}}{{{v_1}}} = \dfrac{1}{6}hr \\\

Similarly, for the next kilometer, he walks at a speed of 8 kilometers per hour, and we could again calculate the time taken by him for the next kilometer
${v_2} = 8km/hr,{d_2} = 1km$
$\therefore {t_2} = \dfrac{{{d_2}}}{{{v_2}}} = \dfrac{1}{8}hr$
Now, we have the total time taken by him to cover the total distance. We can use this to calculate the average speed of the man for the walk
$\therefore t = {t_1} + {t_2} = \dfrac{1}{6} + \dfrac{1}{8} = \dfrac{{4 + 3}}{{24}} = \dfrac{7}{{24}}hr$

spee{d_{average}}\left( v \right) = \dfrac{{dis\tan c{e_{total}}\left( d \right)}}{{tim{e_{total}}\left( t \right)}} \\\ \therefore {v_{average}} = \dfrac{2}{{\left( {\dfrac{7}{{24}}} \right)}} = 2 \times \dfrac{{24}}{7} = \dfrac{{48}}{7}km/hr = 6.86km/hr \\\

Note:
While calculating the average speed, always keep in mind that average speed is not the average of the two speeds with which the man walks for the first two kilometers, It is the total distance covered by him divided by the total time taken.