Two pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute. The other is already filled with 10 gallons, and it is continuing to fill at a rate of 4 gallons per minute. Write an equation to show when the two vats will have an equal amount of liquid.
Use x as your variable.
The first vat is filling at a rate of 6 gallons per minute, so after x minutes, it will have x * 6 gallons of liquid.
The second vat is already filled with 10 gallons and filling at a rate of 4 gallons per minute, so after x minutes, it will have 10 + x * 4 gallons of liquid.
To find the time when the two vats will have an equal amount of liquid, we can set these two expressions equal to each other:
x * 6 = 10 + x * 4
Simplifying the equation:
6x = 10 + 4x
Subtracting 4x from both sides:
6x - 4x = 10
2x = 10
Dividing both sides by 2:
x = 5
Therefore, the two vats will have an equal amount of liquid after 5 minutes.
Two pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute. The other is already filled with 10 gallons, and it is continuing to fill at a rate of 4 gallons per minute.
Write an equation to show when the two vats will have an equal amount of liquid. Use x as your variable.
The equation to show when the two vats will have an equal amount of liquid is:
6x = 10 + 4x
Where:
- 6x represents the amount of liquid in the first vat after x minutes.
- 10 represents the initial amount of liquid in the second vat.
- 4x represents the amount of liquid in the second vat after x minutes.
Simplifying the equation:
6x - 4x = 10
2x = 10
Dividing both sides by 2:
x = 5
Therefore, the two vats will have an equal amount of liquid after 5 minutes.
A yoga studio has two participation plans. For the first plan, the cost is $8 per visit. For the second plan, the cost is $40 per month, and $2 per visit. Write an equation to show the number of visits per month that it would take for the two plans to be equal. Use x as your variable.
For the first plan, the cost is $8 per visit, so the total cost for x visits can be represented by the equation:
Cost of first plan = 8x
For the second plan, the cost is $40 per month, plus $2 per visit. Let's assume x visits in a month. The total cost for x visits can be represented by the equation:
Cost of second plan = 40 + 2x
Now, to find the number of visits per month that it would take for the two plans to be equal, we can set the two equations equal to each other:
8x = 40 + 2x
Simplifying the equation:
6x = 40
Dividing both sides by 6:
x = 40/6
x = 20/3
Therefore, it would take approximately 20/3 visits, or approximately 6.67 visits, per month for the two plans to be equal.
Two pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute. The other vat already contains 28 gallons and is continuing to fill at a rate of 4 gallons per minute. When will the two vats have the same amount of liquid?
They will have the same amount of liquid after ____ minutes.
Let's assume the time it takes for the two vats to have the same amount of liquid is represented by the variable x.
The first vat is empty and filling at a rate of 6 gallons per minute, so after x minutes it will have x * 6 gallons of liquid.
The second vat already contains 28 gallons and is filling at a rate of 4 gallons per minute, so after x minutes it will have 28 + x * 4 gallons of liquid.
To find when the two vats have the same amount of liquid, we can set the two expressions equal to each other:
x * 6 = 28 + x * 4
Simplifying the equation:
6x = 28 + 4x
Subtracting 4x from both sides:
6x - 4x = 28
2x = 28
Dividing both sides by 2:
x = 14
Therefore, the two vats will have the same amount of liquid after 14 minutes.
A yoga studio has two participation plans. The first plan costs $10 per visit. The second plan costs $30 per month, and $4 per visit. How many visits would make the cost of both plans the same?
The plans would cost the same at ____ visits.
Let's assume the variable x represents the number of visits.
For the first plan, the cost is $10 per visit, so the total cost for x visits can be represented by the equation:
Cost of first plan = 10x
For the second plan, the cost is $30 per month, plus $4 per visit. Let's assume x visits. The total cost for x visits can be represented by the equation:
Cost of second plan = 30 + 4x
Now, we can set the two equations equal to each other to find the number of visits that would make the cost of both plans the same:
10x = 30 + 4x
Simplifying the equation:
6x = 30
Dividing both sides by 6:
x = 30/6
x = 5
Therefore, the cost of both plans would be the same at 5 visits.
In a bike race, bike A is 50 miles from the starting point and travels 30 miles per hour. Bike B is 100 miles from the starting point and travels 25 miles per hour. After how many miles will bike A and bike B be the same distance from the starting point?
___ miles