Solving proportion problems involving three quantities How do you solve proportion if 3 variables are given? I have looked in this site but i could not undertand it completely http://www.beatthegmat.com/ratio-proportion-3-variables-t34902.html 15 robots can make a train in 6 days working 5 hours a day. In how many days will 25 robots, working 6 hours a day complete the same work?
 A: 15 robots -> 6 days -> 5 hours
25 robots -> x days -> 6 hours
The first step, you need to find out how many days will be took to create the robot in 6 days again, but in 6 hours, such that:
15 robots -> 6 days -> 5 hours
X robots -> 6 days -> 6 hours
By using proportion, we got 15/X = 6/5, which is X= 12.5 robots
Now, we got two equations involving 6 hours, such that:
25 robots -> x days -> 6 hours
12.5 robots -> 6 days -> 6 hours
By using proportion again, we got 
25/12.5 = 6/x
x = 3 days
A: Robots   Hours   Days
 15       5       6
 25       6       x



*

*More robots, less days: indirect variation.

*More hours, less days: indirect variation.
$$15/25\cdot 5/6 = x/6$$
$$1/2=x/6$$
$$x=3$$

A: You start with $x=6 [\texttt{days}]\times \ldots $
Then you have 2 pairings of 4 numbers. hours $(5/6)$ and robots $(15/25)$. 
Now, you can write a fraction of the two number of a pair. The question is, does it take longer to complete the work, if it is worked 6 hours a day instead of 5 hours a day ? The answer is no. Therefore the factor (fraction) has to be samller than 1. This is the case, if the numerator is smaller than the denominator. Therefore the fraction is $\frac{5}{6}<1$. Similar thoughts can be made with the amount of robots. You have now more robots. More robots means less time to finish the work. Thus the fraction is $\frac{15}{25}<1$.
In total you get $x=6 [\texttt{days}]\times \frac{5}{6} \times \frac{15}{25}$
A: Each robot works for $30$ hours, we have $15$ robots, so to build a train takes $450$ hours.
If we have $25$ robots, they need to each work $\frac{450}{25}=18\text{hours}$.
As they each work for $6$ hours a day, they need to work for $3$ days.
