# If 6 tractors take 6 days to collect the harvest, then how many days will it take 18 tractors to collect the harvest?

Jun 3, 2018

2 days

#### Explanation:

Assuming they work at the same rate and are in direct proportion:
$6 = 6 d$

Where $1$ is multiplied, the other is divided. So to find out how long $1$ worker takes, divide by $6$ to get $1$, multiply by $6$ to get $36 d$.

$1 = 36 d$

Now multiply $1$ by $18$, divide $36 d$ by $18$ to get $2 d$:

$18 = 2 d$

Jun 3, 2018

$2$ days

#### Explanation:

This is an example of inverse proportion.

Where there are two quantities and one increases, the other will decrease. As there is a task to be completed (the harvesting), the MORE tractors that are doing the work, the LESS time it will take to do the job.

$x \times y = k$

For $6$ tractors and $6$ days: $k = 6 \times 6 = 36$

If there are $3$ times as many tractors, the job will be done in $\frac{1}{3}$ of the time.

$x = \frac{36}{y}$

$\frac{36}{18} = 2$ days