A student goes from his house to his friend's house with speed v1. Finding the door of his friend's closed,return back to his own house with the speed v2. Then the average speed of the student is 

Asked by Anil | 28th May, 2017, 06:28: PM

Expert Answer:

Let the distance between the student's house and the house of his friend be X.
The speed of the onward journey is v1.
Hence, the time taken to complete this journey is
 
begin mathsize 12px style straight t subscript 1 equals straight X over straight v subscript 1 end style
 
Now, the return journey is with a speed v2.
Hence, the time taken is
 
begin mathsize 12px style straight t subscript 2 equals straight X over straight v subscript 2 end style
 
The total distance covered in the journey is X + X = 2X
and the total time is t1 + t2.
 
Therefore, the average speed is
 
begin mathsize 12px style straight v subscript av equals fraction numerator Total space distance space covered over denominator Total space time space taken end fraction
straight v subscript av equals fraction numerator 2 straight X over denominator begin display style straight X over straight v subscript 1 end style plus begin display style straight X over straight v subscript 2 end style end fraction equals fraction numerator 2 straight X over denominator straight X open parentheses begin display style 1 over straight v subscript 1 end style plus begin display style 1 over straight v subscript 2 end style close parentheses end fraction
straight v subscript av equals fraction numerator 2 over denominator begin display style fraction numerator straight v subscript 1 plus straight v subscript 2 over denominator straight v subscript 1 straight v subscript 2 end fraction end style end fraction equals fraction numerator 2 straight v subscript 1 straight v subscript 2 over denominator straight v subscript 1 plus straight v subscript 2 end fraction end style

Answered by Romal Bhansali | 1st Nov, 2017, 11:50: AM