Time, speed and distance — Quant Aptitude Questions & Formulas

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Time, Speed & Distance

Everything comes from

D = S \times T

Unit conversion: km/hr → m/s multiply by

\frac{5}{18}

; m/s → km/hr multiply by

\frac{18}{5}

Average Speed

Average speed

= \dfrac{\text{total distance}}{\text{total time}}

— never the average of the speeds.

Equal distance, two speeds:

\dfrac{2xy}{x+y}

Equal distance, three speeds:

\dfrac{3xyz}{xy+yz+zx}

Relative Speed

Same direction:

S_1 - S_2

. Opposite directions:

S_1 + S_2

Early / Late Shortcut

D = \frac{S_1 \times S_2}{\lvert S_1 - S_2\rvert}\times \Delta T

\Delta T

= total time gap (add the early + late minutes), converted to hours.

Trains

Crossing a point (pole / man): distance

= L_1

Crossing a length (platform / bridge): distance

= L_1 + L_2

Boats & Streams

Downstream

D = B + S

; upstream

U = B - S

. Hence

B = \dfrac{D+U}{2}

and .

More Hacks

Cross-over after meeting:

\dfrac{S_1}{S_2} = \sqrt{\dfrac{T_2}{T_1}}