Time and Work Formulas

1. Work Done Formula

$\mathrm{Work}=\mathrm{Time}\times \mathrm{Rate\; of\; Work}$

The total work done is the product of time and rate of work.

2. Time Taken Formula

$\mathrm{Time}=\frac{\mathrm{Work}}{\mathrm{Rate\; of\; Work}}$

The time taken to complete work is the total work divided by the rate of work.

3. Rate of Work Formula

$\mathrm{Rate\; of\; Work}=\frac{\mathrm{Work}}{\mathrm{Time}}$

The rate of work is the total work divided by the time taken.

4. Combined Work Formula

$\mathrm{Combined\; Rate}=\mathrm{Rate\; of\; A}+\mathrm{Rate\; of\; B}$

If two individuals A and B are working together, their combined rate is the sum of their individual rates.

5. Inverse Proportionality Formula

$\mathrm{Work}\propto \frac{1}{\mathrm{Time}}$

Work is inversely proportional to time when the rate of work is constant.

Average Formulas

1. Basic Average Formula

$\mathrm{Average}=\frac{\mathrm{Sum\; of\; Observations}}{\mathrm{Number\; of\; Observations}}$

The average is calculated as the total sum of observations divided by the number of observations.

2. Weighted Average Formula

$\mathrm{Weighted\; Average}=\frac{\mathrm{Sum\; of\; (Weights\; \times \; Observations)}}{\mathrm{Sum\; of\; Weights}}$

The weighted average considers the relative importance (weights) of each observation.

3. Average Speed Formula

$\mathrm{Average\; Speed}=\frac{2\times \mathrm{Speed\; 1}\times \mathrm{Speed\; 2}}{\mathrm{Speed\; 1}+\mathrm{Speed\; 2}}$

The average speed for a journey with two equal distances but different speeds is calculated using the harmonic mean of the two speeds.

4. Group Average Formula

$\mathrm{Group\; Average}=\frac{\mathrm{Total\; Sum\; of\; Groups}}{\mathrm{Total\; Number\; of\; Groups}}$

The group average is calculated by dividing the total sum of all groups by the total number of groups.

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