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Road surfacing gangs are made up of a fixed number of workers and machines.Three gangs have surfaced 20 km of road in 10 days.How many additional gangs should be brought in if all the work is to be finished in another 15 days and there is still 50 km of road to be surfaced?(You should assume that their work does not interfere with each other.)Please use algebra if possible and state any formulas used.

Answer :

We'll use a compound rule of three to solve your problem:

3 gangs 20km 10 days

x gangs 50 km 15 days

Gangs are directly proportional to the surface and indirectly proportional to the number of days:

[tex]\begin{gathered} \frac{3}{x}=\frac{20}{50}\cdot\frac{15}{10} \\ \frac{3}{x}=\frac{300}{500} \\ \frac{3}{x}=\frac{3}{5} \\ 3x=15 \\ x=5 \end{gathered}[/tex]

So, it's needed 5 gangs to complete the work, in total.

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