A man walks at the speed of 2*1/3 km/hr for 2 hours and then at the speed of 1*1/2km / hr for next 2 hours. Find the distance travelled by the man in 4hrs.
Answers
Answer:
You need the Harmonic Mean of the two speeds: 1/( ( 1/4 + 1/6 )/2 ) km/hr
= 2/( (3+2)/12 ) km/hr
= 24/5 km/hr
= 4.8 km/hr
How did I know to use the Harmonic Mean, rather than the Arithmetic Mean, Geometric Mean, or Root-Mean Square?
The answer is, "Experience (I've come across this sort of question many times before)." In reality, for the first times you meet this sort of problem, you just have to go through the reasoning that the other answers have done. These also give indications as to why the Harmonic Mean route is the one that will work.
Incidentally, does my 1/( ( 1/4 + 1/6 )/2 ) look unclear? Let's try to express it better. Let's define all types of mean as:
f(mean) = ( f(x1) + f(x2) + f(x3) + ... + f(xn) ) / n
Then, the harmonic mean has f(x) = x^{-1}
the arithmetic mean has f(x) = x^1
the root-mean square has f(x) = x^2
and the geometric mean has f(x) = ln(x)
Step-by-step explanation: