Question

If a man travels at 10 km/hr. from A to B and again @15 km/hr. from B to A, find the average speed of man for complete journey.

Answer 1

Hint: The journey is started from point A with speed 10 km/hr. So, we can say that the initial speed of the man is 10 km/hr. and the man completes the journey from point B to point A by travelling with speed of 15 km/hr. So, we can say that the final speed of the man is 15 km/hr.
First we will find the time by using the formula
 $ \Rightarrow $ $ Speed = \dfrac{{Dis\tan ce}}{{Time}} $
And then we will find the average speed using the formula
 $ \Rightarrow {S_{avg}} = \dfrac{{Total\;dis\tan ce}}{{Time\;taken}} $

Complete step-by-step answer:
In this question, we are given that a man travels from point A to point B at a speed of 10 km/hr. and then travels back from B to A at a speed 15 km/hr. We need to find the average speed of the man during this complete journey.
Here, the journey is started from point A with speed 10 km/hr. So, we can say that the initial speed of the man is 10 km/hr. and the man completes the journey from point B to point A by travelling with speed of 15 km/hr. So, we can say that the final speed of the man is 15 km/hr.
 $ \Rightarrow $ Initial speed of Man $ = 10km/hr $
 $ \Rightarrow $ Final speed of Man $ = 15km/hr $
Now, let the distance travelled from point A to B be x, so therefore distance travelled from B to A will also be x. Now, we know that
 $ \Rightarrow Speed = \dfrac{{Dis\tan ce}}{{Time}} $
 $
   \Rightarrow T = \dfrac{D}{S} \\
   \Rightarrow T = \dfrac{x}{{10}} + \dfrac{x}{{15}} \\
   \Rightarrow T = \dfrac{{5x}}{{30}} = \dfrac{x}{6} \;
  $
Now, Total distance $ = x + x = 2x $
Now, average speed is given by
 $ \Rightarrow {S_{avg}} = \dfrac{{Total\;dis\tan ce}}{{Time\;taken}} $
 $
   \Rightarrow {S_{avg}} = \dfrac{{2x}}{{\dfrac{x}{6}}} \\
   \Rightarrow {S_{avg}} = 12 \;
  $
Hence, the average speed of the man will be equal to 12 km/hr.
So, the correct answer is “ 12 km/hr.”.

Note: Average speed is also given by the formula
 $ \Rightarrow {S_{avg}} = \dfrac{{2{v_1}{v_2}}}{{{v_1} + {v_2}}} $
Here, $ {v_1} $ is initial velocity and $ {v_2} $ is the final velocity. Therefore, the average speed of the man will be
 $
   \Rightarrow {S_{avg}} = \dfrac{{2\left( {10} \right)\left( {15} \right)}}{{10 + 15}} \\
   \Rightarrow {S_{avg}} = \dfrac{{300}}{{25}} \\
   \Rightarrow {S_{avg}} = 12 \;
  $
Hence, the average speed of the man will be equal to 12 km/hr.