Aship has sufficient food to supply 600 passengers for 3 weeks. How long would the same food last for 900 passengers?
To solve this problem, we can use the concept of inverse variation.
Let's assume that the number of weeks the food lasts is "x" when there are 900 passengers.
According to the problem, we know that the amount of food supplied is inversely proportional to the number of passengers.
This can be expressed mathematically as:
(food supplied) ∝ 1/(number of passengers)
In equation form:
(food supplied) = k/(number of passengers)
where k is a constant of proportionality.
Now, let's use the given information to find the value of k.
When there are 600 passengers, the food lasts for 3 weeks. Plugging these values into the above equation, we get:
(food supplied) = k/(600) = 3
Simplifying, we find:
k = (600)(3) = 1800
Now, we can use this value of k to find the number of weeks the food will last when there are 900 passengers. Plugging these values into the equation, we get:
(food supplied) = 1800/(900) = 2
Therefore, with 900 passengers, the same food will last for 2 weeks.
To find out how long the same food would last for 900 passengers, we can set up a proportion:
Let x be the number of weeks the food would last for 900 passengers.
We can set up the proportion:
600 passengers / 3 weeks = 900 passengers / x weeks
To solve for x, we can cross multiply:
600 * x = 900 * 3
Simplifying, we get:
600x = 2700
Dividing both sides by 600, we get:
x = 2700 / 600
Simplifying further, we get:
x = 4.5
Therefore, the same food would last for 900 passengers for 4.5 weeks.