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?

Question

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Answer 1

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.

Answer 2

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?

Answer 3

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.