Two pumps are being filled by two different pumps. The first vat has 10 gallons is being filled at a rate of 12 gallons per second. The second vat has 25 gallons and is being filled at a rate of 10 gallons per second. After how many seconds will both vats have the same amount of liquid?
@bot
Let's assume that after t seconds, both vats will have the same amount of liquid.
For the first vat, the amount of liquid after t seconds can be calculated using the formula:
Amount in first vat = 10 + (12 * t) gallons
For the second vat, the amount of liquid after t seconds can be calculated using the formula:
Amount in second vat = 25 + (10 * t) gallons
To find when both vats have the same amount of liquid, we set the two equations equal to each other and solve for t:
10 + (12 * t) = 25 + (10 * t)
Simplifying the equation:
12t - 10t = 25 - 10
2t = 15
t = 15 / 2
t = 7.5 seconds
Therefore, after 7.5 seconds, both vats will have the same amount of liquid.
A movie theater offers a special pricing for membership. The normal cost is $7.50 per ticket. The membership costs $5 per ticket but an initial fee of $25. After how many tickets are both options the same price?
Let's assume x represents the number of tickets.
For the normal price option, the cost of x tickets is given by:
Normal Price = 7.50 * x
For the membership option, the cost of x tickets is given by:
Membership Price = 5 * x + 25
To find when both options are the same price, we set the two equations equal to each other and solve for x:
7.50 * x = 5 * x + 25
Subtracting 5 * x from both sides of the equation:
2.50 * x = 25
Dividing both sides of the equation by 2.50:
x = 25 / 2.50
x = 10
Therefore, after purchasing 10 tickets, both the normal price and membership price will be the same.
To find out after how many seconds both vats will have the same amount of liquid, we need to set up an equation.
Let's assume that t represents the number of seconds.
The amount of liquid in the first vat after t seconds can be calculated using the equation:
Amount = Initial amount + (Rate * t)
For the first vat, the amount of liquid after t seconds would be:
Amount1 = 10 + (12 * t)
Similarly, for the second vat, the amount of liquid after t seconds would be:
Amount2 = 25 + (10 * t)
To find when the amounts in both vats will be equal, we need to set up an equation and solve for t:
Amount1 = Amount2
10 + (12 * t) = 25 + (10 * t)
Now, let's solve the equation:
12t - 10t = 25 - 10
2t = 15
t = 15 / 2
t = 7.5 seconds
Therefore, both vats will have the same amount of liquid after 7.5 seconds.
To find out when both vats will have the same amount of liquid, we can set up an equation based on their fill rates and current levels.
Let's assume that after t seconds, both vats will have the same amount of liquid. At that time, the first vat will have 10 + (12t) gallons, and the second vat will have 25 + (10t) gallons.
Setting up the equation: 10 + (12t) = 25 + (10t)
First, simplify the equation by combining like terms: 12t - 10t = 25 - 10
2t = 15
Now, isolate t by dividing both sides of the equation by 2: t = 15/2
Therefore, after 15/2 or 7.5 seconds, both vats will have the same amount of liquid.