A group of 48 ants have food for 16 days but 12 ants died after 4 days due to rain. For how many days the remaining food will be enough
there are 48*16 food portions
after 4 days, 48*4 portions have been eaten.
So, there is enough for (48*16 - 48*4)/(48-12) = 16 days
or, after 4 days, 1/4 of the food is eaten. That leaves enough for 12 days for the full population. But, the population is now 3/4 what it was, meaning it will last 4/3 as long, or 16 more days.
16
To determine how many days the remaining food will last for the remaining ants, we'll start by calculating the rate at which the food is consumed by the ants.
If a group of 48 ants have enough food for 16 days, we can find the total amount of food by multiplying the number of ants (48) by the number of days (16):
Total amount of food = 48 ants * 16 days = 768 ant-days
After 4 days, 12 ants died due to rain. Therefore, the number of ants remaining is 48 - 12 = 36 ants.
To find out how many days the remaining food will last, we divide the total amount of food by the number of ants remaining:
Remaining food consumption rate = Total amount of food / Number of ants remaining
Remaining food consumption rate = 768 ant-days / 36 ants = 21.33 ant-days per ant
Since the food consumption rate is 21.33 ant-days per ant, we can calculate the number of days the remaining food will last for the remaining ants:
Number of days remaining food will last = Remaining food / Remaining food consumption rate
Number of days remaining food will last = 768 ant-days / 21.33 ant-days per ant ≈ 36 days
Therefore, the remaining food will be enough for approximately 36 days for the remaining ants.
To find out how many days the remaining food will be enough for the remaining ants, we first need to calculate the daily food consumption per ant.
Start by dividing the total food supply by the number of days it is meant to last.
Total food supply = 48 ants * 16 days = 768 ant-days
Next, find the food consumption of each ant per day:
Food consumption per ant per day = Total food supply / total number of ant-days = 768 ant-days / 48 ants = 16 ant-days per ant per day
Since 12 ants died after 4 days, there are now 48 - 12 = 36 ants remaining.
To find out how long the remaining food supply will last for the remaining 36 ants, divide the remaining food supply by the daily food consumption per ant:
Remaining food supply = Food consumption per ant per day * remaining number of days * remaining number of ants = 16 ant-days per ant per day * (16 - 4) days * 36 ants
Remaining food supply = 12 * 36 = 432 ant-days
Therefore, the remaining food will be enough for the 36 remaining ants for 12 days.
Well, isn't that just a regular picnic for ants? Rain or shine, they managed to gather enough food to last them 16 days. But unfortunately, 12 of their little buddies met their demise during those rainy days. So, if we subtract those 12 ant-sized appetites from the group, the remaining food should last even longer! Let's do some calculations.
Now we have 48 ants - 12 ants = 36 ants.
Since the remaining food was initially enough for 48 ants for 16 days, we can use a simple proportion to find out how long it will last for 36 ants.
48 ants : 16 days = 36 ants : x days
Cross-multiplying, we get 48x = 36 * 16, which simplifies to 48x = 576.
Divide both sides by 48, and we find that x = 576 / 48 = 12 days.
So, hooray for the surviving ants! They can still have a food party for 12 more days before they need to go on another grocery run.