 maths > commercial-arithmetics

Time and Work

what you'll learn...

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$$12$ days.

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

Unitary method in time-work:
The work completed in $1$$1$ unit time is the work-rate.

A person completes a building in $12$$12$ days.
The work-rate of the person is $\frac{1}{12}$$\frac{1}{12}$ of a building per day.

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

work rate $×$$\times$ time $=$$=$ work done
Work-rate and work done are given. Time is to be calculated.

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

A person works at $\frac{1}{22}$$\frac{1}{22}$ building per day. How many buildings he would have completed in $77$$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$$77$ days $=77×\frac{1}{22}=3.5$$= 77 \times \frac{1}{22} = 3.5$

A person completes $2$$2$ buildings in $30$$30$ days. How many buildings she would complete if she works for $75$$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$$75$ days $=\frac{2}{30}×75=5$$= \frac{2}{30} \times 75 = 5$

A person completes a building at $\frac{1}{35}$$\frac{1}{35}$ building per day and completes $2$$2$ buildings in the given time. If the work-rate is increased to $\frac{1}{7}$$\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}$$\frac{1}{7}$ building per day $=2÷\frac{1}{35}×\frac{1}{7}=10$$= 2 \div \frac{1}{35} \times \frac{1}{7} = 10$ buildings.

A person completes $\frac{1}{40}$$\frac{1}{40}$ of a building per day and takes $120$$120$ days to complete a set of buildings. If the work rate is increased to $\frac{1}{30}$$\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}×120÷\frac{1}{30}=90$$= \frac{1}{40} \times 120 \div \frac{1}{30} = 90$ days

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

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

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

If they work together, the combined work rate
$=\frac{1}{20}+\frac{1}{30}$$= \frac{1}{20} + \frac{1}{30}$
$=\frac{5}{60}$$= \frac{5}{60}$
$=\frac{1}{12}$$= \frac{1}{12}$

workrate $×$$\times$ time $=$$=$ work
$\frac{1}{12}×$$\frac{1}{12} \times$ time $=$$=$5 buildings
time $=5×\frac{12}{1}$$= 5 \times \frac{12}{1}$
$=60$$= 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