Both distances 3966 and 4746 were done in 6 hours, so the speeds are:
speed against wind = 3966/6=661 km/h (difference of airplane and wind)
speed with wind = 4746/6=791 km/h (sum of airplane and wind)
The speed of airplane is greater than that of the wind, so this is a sum and difference problem.
Greater speed (plane) = (sum+difference)/2=(791+661)/2=726 km/h
Lesser speed (wind) = (sum-difference)/2 = (791-661)/2 = 65 km/h
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It not the middle of a and c
Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.
The relation 2+4+6+...+2n = n^2+n has to be proved.
If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2
Assume that the relation holds for any value of n.
2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)
= n^2 + n + 2n + 2
= n^2 + 2n + 1 + n + 1
= (n + 1)^2 + (n + 1)
This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.
<span>By mathematical induction the relation is true for any value of n.</span>
