Time and Work

overview

An example to the rate $\times$ span $=$ aggregate, is

work-rate $\times$ time $=$ work-done.

This is explained in detail.

examples with work

A person completes a building in $12$ days.

Her work rate $=\frac{1}{12}$ 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 $\frac{1}{12}$ of a building per day.

A person works at $\frac{1}{20}$ building per day. How long does the person take to complete $3$ buildings?

work rate $\times$ time $=$ work done

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

Time to complete $3$ buildings $=3\xf7\frac{1}{20}=60$ days.

A person works at $\frac{1}{22}$ building per day. How many buildings he would have completed in $77$ days?

work rate $\times$ time $=$ work done

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

The number of buildings he would have completed in $77$ days $=77\times \frac{1}{22}=3.5$

A person completes $2$ buildings in $30$ days. How many buildings she would complete if she works for $75$ days?

work rate $\times$ time $=$ work done

Time and work done are in direct variation.

The number of buildings she would complete if she works for $75$ days $=\frac{2}{30}\times 75=5$

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

work rate $\times$ time $=$ work done

work rate and work done are in direct variation.

The number of building he would complete if the work rate is increased to $\frac{1}{7}$ building per day $=2\xf7\frac{1}{35}\times \frac{1}{7}=10$ buildings.

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

work rate $\times$ time $=$ work done

work rate and time are in inverse variation.

The number of days he would take $=\frac{1}{40}\times 120\xf7\frac{1}{30}=90$ days

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?

work rate of Person $A=\frac{2}{40}=\frac{1}{20}$

work rate of person $B=\frac{1}{30}$

If they work together, the combined work rate

$=\frac{1}{20}+\frac{1}{30}$

$=\frac{5}{60}$

$=\frac{1}{12}$

workrate $\times$ time $=$ work

$\frac{1}{12}\times$ time $=$5 buildings

time $=5\times \frac{12}{1}$

$=60$ days.

summary

**Problems in Time-Work** : Simplify the problem to

*work rate $\times$ time $\Rightarrow$ 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)

Outline

The outline of material to learn "commercial arithmetics" is as follows.

Note: * Click here for the detailed ouline of commercial arthmetics.*

• **Ratio, Proportion, Percentage**

→ __Comparing Quantities__

→ __Introduction to Ratio__

→ __Ration & Fraction Differences__

→ Proportions__P__

→ __Percentages__

→ __Conversion to percentage__

• **Unitary Method**

→ __Introduction to Unitary Method__

→ __Direct Variation__

→ __Inverse Variation__

→ __DIV Pair__

• **Simple & Compound Interest**

→ __Story of Interest__

→ __Simple Interest__

→ __Compound Interest__

• **Rate•Span=Aggregate**

→ __Understanding Rate-Span__

→ __Speed • Time=Distance__

→ __Work-rate • time = Work-amount__

→ __Fill-rate • time = Filled-amount__

• **Profit-Loss-Discount-Tax**

→ __Profit-Loss__

→ __Discount__

→ __Tax__

→ __Formulas__