# If six workers complete 1 km of roadway in four days, how long would it take four workers to complete 3 km of roadway?

May 24, 2018

18 days

#### Explanation:

Assuming each of the workers has the same impact then we need to find the impact of the single worker per day. The solution to this is rather simple but easy to miss, since we have 6 workers and in 4 days or 96 hours they can complete 1 km of roadway or 1000 meters of roadway.To find the impact of one we divide the km with the days $\frac{1000}{4} = 166.66$ and then we divide that with 6 to find the individual impact of the workers. So that is$\frac{250}{6} = 41.66$. That amount of roadway is the one that a single worker can complete in one day. Now for 4 workers we take this amount and multiple it by 4 and we have their impact for a day. 4*41.66=166.64
Now we need to find how many days it will take them to make the roadway so we multiple by 18 and we find a number(2999.52) really close to 3000. That happens because the divination $\frac{1000}{6} = 166.6666666667$ and we only took as an answer the 166.66. So the answer is 18 days. If we multiple $166.6666666667 \cdot 18 = 3000$ to ensure that we are doing everything right.

May 24, 2018

18 days

#### Explanation:

$\textcolor{b l u e}{\text{Initial condition: 6 people, 4 days and 1 km of road.}}$

$\textcolor{b r o w n}{\text{If you are ever not sure what to do look at the units of measurements}}$
$\textcolor{b r o w n}{\text{How ever you manipulate the units to get to the answer you do}}$$\textcolor{b r o w n}{\text{the same to the numbers}}$

$1 \textcolor{w h i t e}{\text{d")km " with " 6" people" -> 1/6 (km)/("person}}$

This was over 4 days so each person's output for 1 day is:

$\frac{1}{6} \frac{k m}{\text{person")-:(4" days") ->1/24 (km)/("person day}}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{New condition: 4 people and 3 km road}}$

ubrace(1/24 (km)/(cancel("person")cancel( "day")))xx ubrace(cancel("person count"))xxubrace(cancel("day count"))=3 color(white)("d")km

$\textcolor{w h i t e}{\text{ddddd")1/24color(white)("ddddd")xxcolor(white)("ddddd")4color(white)("ddddd")xxcolor(white)("dddd")dcolor(white)("dddd}} = 3$

$\textcolor{w h i t e}{\text{d}}$
$\textcolor{w h i t e}{\text{d}}$

$\frac{4}{24} d = 3$

$\frac{1}{6} d = 3$

$d = 3 \times 6 = 18$