Paula has two fish tanks that are leaking. The first fish tank holds 50 gallons of water and is leaking at a rate of 5 gallons per day. The second fish tank holds 90 gallons of water and is leaking at a rate of 15 gallons per day.
At how many days will the two fish tanks have the same amount of water in them?
a 4
b 5
c 3
d 12
Let's assume that after "x" days, both fish tanks will have the same amount of water in them.
After "x" days, the first fish tank will have 50 - 5x gallons of water remaining.
After "x" days, the second fish tank will have 90 - 15x gallons of water remaining.
To find the number of days where both fish tanks have the same amount of water, we can set the remaining water in the first fish tank equal to the remaining water in the second fish tank and solve for "x":
50 - 5x = 90 - 15x
10x = 40
x = 4
Therefore, the two fish tanks will have the same amount of water in them after 4 days. Answer: a) 4.
To find the number of days when both fish tanks have the same amount of water, we need to determine when the amount of water lost in each tank is equal.
Let's assume 'd' represents the number of days.
For the first fish tank, the total water lost in 'd' days is 5 gallons per day multiplied by 'd': 5d.
For the second fish tank, the total water lost in 'd' days is 15 gallons per day multiplied by 'd': 15d.
The equation to equate the amount of water lost in both tanks is:
5d = 15d
To solve this equation, we can subtract 5d from both sides:
0 = 10d
Since we can't divide by zero, we know that the amount of water lost will never be equal for both tanks since they have different leak rates. Therefore, the two fish tanks will never have the same amount of water in them.
Therefore, the correct answer is none of the given options.
To find out at how many days the two fish tanks will have the same amount of water, we need to set up an equation to represent the amount of water in each tank over time.
Let's denote the number of days as 'd', and the amount of water in the first tank at any given day as 'W1', and in the second tank as 'W2'.
For the first tank, which originally holds 50 gallons of water and leaks 5 gallons per day, the amount of water in the first tank after 'd' days can be represented as:
W1 = 50 - 5d
For the second tank, which originally holds 90 gallons of water and leaks 15 gallons per day, the amount of water in the second tank after 'd' days can be represented as:
W2 = 90 - 15d
To find the number of days where the two tanks have the same amount of water, we need to set up an equation by equating the two expressions for 'W1' and 'W2', and solve for 'd':
50 - 5d = 90 - 15d
Now, let's solve this equation:
50 - 5d + 15d = 90
10d = 40
d = 40/10
d = 4
Therefore, at 4 days, the two fish tanks will have the same amount of water.
So, the correct answer is option a) 4.