Time, Speed & Distance

At a glance 11 formulas

1. 1Distance, speed, time$D = S \times T$$1\ \text{km/h} = \tfrac{5}{18}\ \text{m/s}$
2. 2Average speed$\bar{S} = \dfrac{\text{total distance}}{\text{total time}}$
3. 3Same distance, two speeds$\bar{S} = \dfrac{2xy}{x + y}$$\text{equal times at each: } \bar{S} = \dfrac{x + y}{2}$
4. 4Relative speed$\text{towards: } a + b \qquad \text{same way: } a - b$
5. 5Meet or catch up$T = \dfrac{\text{gap}}{\text{relative speed}}$$\text{head start} = \text{leader's speed} \times \text{lead time}$
6. 6Times after meeting$\dfrac{S_A}{S_B} = \sqrt{\dfrac{t_B}{t_A}}$$\text{they met after } \sqrt{t_A\, t_B}$
7. 7Meeting twice$D = 3d_1 - d_2$$d_1 \text{ from one end, then } d_2 \text{ from the other}$
8. 8Ratio method$D\ \text{fixed: } T_1 : T_2 = S_2 : S_1$$T\ \text{fixed: } D_1 : D_2 = S_1 : S_2$
9. 9Slower than usual$S \times \tfrac{a}{b} \Rightarrow \text{delay} = \tfrac{b - a}{a}\, T$$S \times \tfrac{b}{a} \Rightarrow \text{saving} = \tfrac{b - a}{b}\, T$
10. 10Late and early$D = \dfrac{S_1 S_2}{S_1 - S_2} \times \Delta T$$\Delta T = \text{late} + \text{early};\ \text{both late or both early: the difference}$
11. 11Stops per hour$\text{min} = \dfrac{\text{speed lost}}{\text{non-stop speed}} \times 60$