7.59. Five workers together can build a road in 20 days. Suppose every worker works at the same rate. If three workers work on the road for 10 days before eleven more workers join them, then how long total will it take to build the road?
Hint: Problems involving rates and work can often be solved by thinking about how much work is done per unit of time.
Hint: How long would it take one worker to build the whole road? What fraction of the road does one worker complete in one day?

Five workers together can build a road in 20 days. Suppose every worker works at the same rate. If three workers work on the road for 10 days before eleven more workers join them

Find:

the numbers of days it takes to complete the work

Step 1 of 1

Because 5 workers can build a road in 20 days, each worker can build [tex]$\frac{1}{5}$[/tex] of a road in 20 days.

Therefore, each worker can build 1 road working alone in [tex]$20 \cdot 5=100$[/tex] days.

So, each worker builds [tex]$\frac{1}{100}$[/tex] road each day.

Therefore, three workers together build [tex]$\frac{3}{100}$[/tex] of a road each day, so in 10 days they build $10.

[tex]$\frac{3}{100}=\frac{3}{10}$[/tex] of a road.

At this point, they have [tex]$1-\frac{3}{10}=\frac{7}{10}$[/tex] of the road to the finish.

After the 11 extra workers join in, the 14 workers build [tex]$\frac{14}{100}$[/tex] of the road each day.

So, to finish the remaining [tex]$\frac{7}{10}$[/tex] of a road, the workers must work for

[tex]$\begin{aligned}\frac{\frac{7}{10} \text { road }}{\frac{14}{100} \frac{\text { ruad }}{\text { day }}} &=\frac{7}{10} \cdot \frac{100}{14} \text { days } \\&=5 \text { days. }\end{aligned}$[/tex]

Therefore, the road is built in 10+5=15 days