Time, Speed and Distance — CDS Elementary Mathematics

Formulas (2)

• Average speed · Equal distances
  $$\bar v = \dfrac{2ab}{a + b}$$
• Speed and time over a fixed distance · Fixed distance
  $$v_1 t_1 = v_2 t_2$$

Watch out for (2)

• Not the average of the speeds
  → Average speed
• Early plus late
  → Speed and time over a fixed distance

Formulas (2)

• Faster speed, less time · Speed change
  $$\dfrac dv - \dfrac{d}{v + x} = y \;\Rightarrow\; v(v + x) = \dfrac{dx}{y}$$
• Two conditions, two unknowns · Linear in reciprocals
  $$\dfrac{d_1}{a} + \dfrac{d_2}{b} = T_1, \quad \dfrac{e_1}{a} + \dfrac{e_2}{b} = T_2$$

Watch out for (2)

• Slower means more time
  → Faster speed, less time
• Solve for the reciprocals
  → Two conditions, two unknowns

Formulas (2)

• Chasing: the same direction · Catching up
  $$t = \dfrac{\text{gap}}{u - v}$$
• Meeting: opposite directions · After meeting
  $$\dfrac uv = \sqrt{\dfrac{t_2}{t_1}}$$

Watch out for (2)

• After the theft or after the start?
  → Chasing: the same direction
• Distance from which end?
  → Meeting: opposite directions

Formulas (2)

• Passing poles, platforms and bridges · Crossing time
  $$t = \dfrac{L + P}{v}$$
• Trains passing moving objects · Relative crossing
  $$t = \dfrac{L_1 + L_2}{u \pm v}$$

Watch out for (2)

• Clearing the last stone
  → Passing poles, platforms and bridges
• A man in a train is a point
  → Trains passing moving objects

Formulas (1)

• Downstream and upstream · Boat and stream
  $$b = \dfrac{d + u}{2}, \qquad s = \dfrac{d - u}{2}$$

Watch out for (1)

• Half the difference, not the difference
  → Downstream and upstream

Formulas (1)

• Starts, beats and laps · Beat by a distance
  $$v_A : v_B = D : (D - x)$$

Watch out for (1)

• Count only complete laps
  → Starts, beats and laps

Formulas (1)

• Angles between the hands · Angle between the hands
  $$\theta = |30h - 5.5m|$$

Watch out for (1)

• The hour hand moves too
  → Angles between the hands