- Rajesh traveled from city A to city B covering as much distance in the
second part as he did in the first part of this journey. His speed during
the second part was twice as that of the speed during the first part of the
journey. What is his average speed of journey during the entire travel?
(1) His average speed is the harmonic mean of the individual speeds for the two parts. (2) His average speed is the arithmetic mean of the individual speeds for the two parts. (3) His average speed is the geometric mean of the individual speeds for the two parts. (4) Cannot be determined.
Solution:
The first part is 1/3rd of the total distance and the second part is 2/3rd of
the total distance. He travels at s km/hr speed during the first half and 2s
km/hr speed during the second half.
If 3 km is the total distance, then 1 km was traveled at s km/hr and 2 kms was
traveled at 2s km/hr speed.
Hence average speed =
Total Distance / Total Time = [ 3 / (1/s + 2/s) ] = 3 / ( 4 / 2s ) = 3s / 2.
This, however, = s+2s / 2 = 3s / 2
which is the arithmetic mean of the speeds of the two parts.
