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<p>A contractor was awarded a tender to construct $4$ houses within $180$ days.  He hired $24$ men for the job.  After $60$ days, he found that they had completed only $1$ house. Each hired man works at the same constant rate. How many more men should he employ to complete the job within $180$ days?</p>

A contractor was awarded a tender to construct $4$ houses within $180$ days.  He hired $24$ men for the job.  After $60$ days, he found that they had completed only $1$ house. Each hired man works at the same constant rate. How many more men should he employ to complete the job within $180$ days?

Combined Proportion

Work Rate Problem: Construction of Houses

Direct and Inverse Proportion

<p>$15$ carpenters can finish making $45$ tables in $27$ days.</p>
<ol class="abc-list"><li data-list-item-id="item-1764482728982-5w7qcwwd3" data-list-item-path="item-1764482728982-5w7qcwwd3"><div class="list-item-paragraph">Find how many carpenters would be needed if&nbsp;$63$ tables are to be made in $81$ days.</div></li><li data-list-item-id="item-1764482730716-0bbirq517" data-list-item-path="item-1764482730716-0bbirq517"><div class="list-item-paragraph">After working for&nbsp;$9$ days, $4$ of the carpenters resigned and the job was completed by<br>the remaining carpenters.  Find the total number of days it will take to make the $63$ tables.<br></div></li></ol>
<p>Assume every carpenter works at the same constant rate, with unchanged working hours per day, and all tables require the same amount of work.</p>

$15$ carpenters can finish making $45$ tables in $27$ days.

Assume every carpenter works at the same constant rate, with unchanged working hours per day, and all tables require the same amount of work.

Combined Proportion: Carpenters, Time and Output

<p>If&nbsp;$4$ duplicating machines can print $3000$ pages of paper in $3$ hours, calculate the number of pages that&nbsp;$3$ similar duplicating machines can print in $5$ hours.</p>
<p>Assume every machine prints at the same constant rate throughout.</p>

If $4$ duplicating machines can print $3000$ pages of paper in $3$ hours, calculate the number of pages that $3$ similar duplicating machines can print in $5$ hours.

Assume every machine prints at the same constant rate throughout.

Combined Proportion: Machines, Time and Output

<p>Two workers can decorate a meeting room measuring $5.5$ m by $12$ m by $2$ m in $3$ hours. Assuming that they all work at the same rate for the same number of hours per day, find</p>
<ol class="i-list"><li data-list-item-id="item-1760783499263-kfw4ayti5" data-list-item-path="item-1760783499263-kfw4ayti5"><div class="list-item-paragraph">the number of workers needed to decorate a meeting room measuring $3$ m by $11$ m by $24$ m in $3$ hours,</div></li><li data-list-item-id="item-1760783499998-mwrknszbh" data-list-item-path="item-1760783499998-mwrknszbh"><div class="list-item-paragraph">the number of workers needed to decorate the bigger meeting room in $1$ hour.</div></li></ol>
<p>Model check: the room dimensions alone do not specify the amount of decorating work. The answers below assume that work is proportional to room volume, with each worker maintaining the same constant rate. If work instead depends on wall or ceiling area, more information is needed.</p>

Two workers can decorate a meeting room measuring $5.5$ m by $12$ m by $2$ m in $3$ hours. Assuming that they all work at the same rate for the same number of hours per day, find

Model check: the room dimensions alone do not specify the amount of decorating work. The answers below assume that work is proportional to room volume, with each worker maintaining the same constant rate. If work instead depends on wall or ceiling area, more information is needed.

IP1U9 Exercise Q4

<p>It takes $4$ workers to paint a house in $1\frac{1}{2}$ days. Assuming the workers paint at the same rate,</p>
<ol class="abc-list"><li><div class="list-item-paragraph">how many days will $3$ workers take to paint the same house?</div></li><li><div class="list-item-paragraph">how many more workers are needed if the house is to be painted in half a day?</div></li><li><div class="list-item-paragraph">how many days will $6$ workers take to paint $5$ such houses?</div></li></ol>

It takes $4$ workers to paint a house in $1\frac{1}{2}$ days. Assuming the workers paint at the same rate,

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