if 12 cats can catch 6 rats in 2 hours, how many hours would it take 50 cats to catch 75 rats
each cat can catch 1/4 rat per hour
so it will take 350 cats to catch 75 rats in 1 hour
so it will take 7 hours for 50 cats to do the job.
To solve this problem, we can set up a proportion to compare the ratios of cats to rats in two different situations.
Let's first determine the ratio of cats to rats in the given situation: 12 cats can catch 6 rats in 2 hours.
12 cats / 6 rats = 2 hours.
Now, let's find the ratio for the unknown situation: 50 cats catching 75 rats.
50 cats / 75 rats = x hours (unknown).
We can set up a proportion using these ratios:
12/6 = 50/75.
To solve for x, we cross-multiply:
12*75 = 6*50.
900 = 300.
Now, solve for x:
x = 900 / 300 = 3 hours.
Therefore, it would take 50 cats to catch 75 rats in 3 hours.
To find the number of hours it would take 50 cats to catch 75 rats, we can set up a proportion:
Number of cats / Number of rats = Number of hours
From the given information, we know that 12 cats can catch 6 rats in 2 hours. Therefore, the rate at which the cats catch rats is 6 rats / 12 cats = 1/2 rat per cat per hour.
Now, to find the number of hours it would take 50 cats to catch 75 rats, we can solve the proportion:
50 cats / 75 rats = x hours / 1 rat
To find x, we cross-multiply and divide:
50 cats * 1 rat = 75 rats * x hours
50/75 = x/1
x = (50/75) * 1
x = 0.67 hours
So, it would take approximately 0.67 hours (or about 40 minutes) for 50 cats to catch 75 rats.