If the ratio of the speeds of \(A\) and \(B\) is \(a: b\), then the ratio of the times taken by them to cover the same distance is \(\frac{1}{a}: \frac{1}{b}\) or \(b: a\).
Suppose a man covers a certain distance at \(x \mathrm{~km} / \mathrm{hr}\) and an equal distance at \(y \mathrm{~km} / \mathrm{hr}\). Then, the average speed during the whole journey is \(\left(\frac{2 x y}{x+y}\right) \mathrm{km} / \mathrm{hr}\).
Suppose two men are moving in the same direction at \(u \mathrm{~m} / \mathrm{s}\) and \(v \mathrm{~m} / \mathrm{s}\) respectively, where \(u>v\), then their relative speed \(=(u-v) \mathrm{m} / \mathrm{s}\).
Suppose two men are moving in opposite directions at \(u \mathrm{~m} / \mathrm{s}\) and \(v \mathrm{~m} / \mathrm{s}\) respectively, then their relative speed \(=(u+v) \mathrm{m} / \mathrm{s}\).
If two persons \(A\) and \(B\) start at the same time in opposite directions from two points and after passing each other they complete the journeys in \(a\) and \(b\) hours respectively, then A’s speed: B’s speed \(=\sqrt{b}: \sqrt{a}\).