There are two different vats. The first vat has 12 gallons and is being filled at a rate of 3 gallons per minute. The second vat has 108 gallons and is leaking fluid at a rate of 7 gallons per minute. After how many seconds will both vats have the same amount of liquid?
Hint: the answer is not 576
To solve this problem, we need to set up a equation to represent the amount of liquid in each vat at any given time.
Let's say t represents the number of minutes that have passed.
For the first vat, the amount of liquid in it can be represented by:
12 + 3t (since it is being filled at a rate of 3 gallons per minute)
For the second vat, the amount of liquid in it can be represented by:
108 - 7t (since it is leaking at a rate of 7 gallons per minute)
Now, we can set up an equation to find when both vats have the same amount of liquid:
12 + 3t = 108 - 7t
Simplifying the equation, we get:
10t = 96
t = 9.6
Since the question asks for the answer in seconds, we need to convert 9.6 minutes to seconds.
There are 60 seconds in a minute, so:
9.6 minutes * 60 seconds/minute = 576 seconds
Therefore, after 576 seconds, both vats will have the same amount of liquid.
It says that 576 is wrong
Apologies for the incorrect response. Let's reevaluate the problem.
The first vat is being filled at a rate of 3 gallons per minute. Let's represent the amount of liquid in the first vat after t minutes as 12 + 3t.
The second vat is leaking fluid at a rate of 7 gallons per minute. Let's represent the amount of liquid in the second vat after t minutes as 108 - 7t.
To find when both vats have the same amount of liquid, we can set the two expressions equal to each other:
12 + 3t = 108 - 7t
Adding 7t to both sides and subtracting 12 from both sides, we get:
10t = 96
Dividing both sides by 10, we find:
t = 9.6
Since the problem asks for the time in seconds, we can multiply 9.6 minutes by 60 seconds/minute:
9.6 minutes * 60 seconds/minute = 576 seconds
Therefore, after 576 seconds, both vats will have the same amount of liquid.
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It's wrong. What do you not understand about an equation being wrong??
Apologies for the incorrect response earlier. Let's reevaluate the problem.
To find the time when both vats have the same amount of liquid, we need to equate the expressions representing the amount of liquid in each vat.
Let t represent the number of minutes.
For the first vat: amount of liquid = 12 + 3t (filled at a rate of 3 gallons per minute)
For the second vat: amount of liquid = 108 - 7t (leaking at a rate of 7 gallons per minute)
Setting these two expressions equal to each other, we have:
12 + 3t = 108 - 7t
Combining like terms:
10t = 96
Dividing both sides by 10:
t = 9.6
Since the problem asks for the time in seconds, we multiply t by 60:
9.6 minutes * 60 seconds/minute = 576 seconds
Therefore, after 576 seconds, both vats will have the same amount of liquid.