An example to the rate `xx` span `=` aggregate, is

work-rate`xx` time `=` work-done.

This is explained in detail.

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A person completes a building in `12` days. What is her work rate?

- `30` days per month
- `1/12` of a building per day
- `1/12` of a building per day

The answer is "`1/12` of a building per day".

Unitary method in time-work:

The work completed in `1` unit time is the work-rate.

A person completes a building in `12` days.

The work-rate of the person is `1/12` of a building per day.

A person works at `1/20` building per day. How long does the person take to complete `3` buildings?

- `60` days
- `60` days
- `20` days

The answer is "`60` days"

work rate `xx` time `=` work done

Work-rate and work done are given. Time is to be calculated.

A person works at `1/22` building per day. How many buildings he would have completed in `77` days?

- `7` buildings
- `3.5` buildings
- `3.5` buildings

The answer is "`3.5` buildings"

work rate `xx` time `=` work done

Work-rate and time are given. Work done is to be calculated.

A person completes `2` buildings in `30` days. How many buildings she would have completed if she works for `75` days?

- `5` buildings
- `5` buildings
- `7` buildings

The answer is "`5` buildings"

work rate `xx` time `=` work done

Time and work done are in direct variation.

A person completes a building at `1/35` building per day and completes `2` buildings in a given time. If the work-rate is increased to `1/7` building per day, how many buildings would he complete?

- `10` buildings
- `10` buildings
- `1/5` buildings

The answer is "`10` buildings"

work rate `xx` time `=` work done

work rate and work done are in direct variation.

A person completes `1/40` of a building per day and takes `120` days to complete a set of buildings. If the work rate is increased to `1/30`, how many days does he take to complete the same?

- `90` days
- `90` days
- `120` days

The answer is "`90` days"

work rate `xx` time `=` work done

work rate and time are in inverse variation.

Person `A` takes `40` days to complete `2` buildings and person `B` takes `30` days to complete `1` building. If they work together, how many days do they take to complete `5` buildings?

- `50` days
- `60` days
- `60` days

The answer is "`60` days".

work rate of Person `A = 2/40 = 1/20`

work rate of person `B = 1/30`

If they work together, the combined work rate

`= 1/20 + 1/30`

`=5/60 `

`=1/12`

workrate `xx` time `=` work

`1/12 xx ` time `= `5 buildings

time `=5 xx 12/1`

`=60` days.

**Problems in Time-Work** : Simplify the problem to *work rate `xx` time `rArr` work done*

There are three quantities in the equation. Possible formulation of questions are

• two are given, and the third is asked.

• two are given. If one of the given is modified, the changed second is asked. (direct or inverse variation)

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