Answer:
The food will last for 16 days
Explanation:
Proportions
We need to know how the variables depend on each other.
It's clear that:
The more campers, the more food the camp needs.
The more time, the more food the camp needs.
Therefore, the amount of food (F) is directly proportional to the number of campers (c) and the time (t).
This can be written as:
F = k.c.t
Where k is a constant that we'll be found by knowing the camp needs F=900 Kg of food for c=40 campers and t=20 days:
900 = k*40*20=800k
Thus:
k=9/8
And:
F = 9/8 c.t
We now need to find how many days will F=540 kg of food will last for c=30 campers. So we solve the equation for t:
t = 8/9 * F/c
t = 8/9 * 540/30
t = 16 days
The food will last for 16 days