What is the answer to 174 divided by 6
2 answers:
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Answer:
50 cats would take 6 hours to catch 75 rats.
Step-by-step explanation:
After reading the statement we noticed the existence of two relationships:
1) <em>The amount of cats is directly proportional to the quantity of caught rats.</em>
2) <em>The amount of cats is inversely proportional to time taken to catch rats. </em>
That is to say:
(Eq. 1)
Where:
- Amount of cats, dimensionless.
- Amount of caught rats, dimensionless.
- Time, measured in hours.
- Proportionality ratio, measured in hours.
Then, we obtain the following relationship by eliminating the proportionality ratio in (Eq. 1):
(Eq. 2)
Where:
,
- Initial and final amounts of cats, dimensionless.
,
- Initial and final amounts of caught rats, dimensionless.
,
- Initial and final times, measured in hours.
Now we clear final time in (Eq. 2):
By knowing that ,
,
,
,
, then we get that time taken by 50 cats to catch 75 rats is:
50 cats would take 6 hours to catch 75 rats.