Two water tanks are being filled. The water in Tank A is 3 inches deep, and the depth of the water increases 4 inches every hour. The water in Tank B is 10 inches deep, and the depth is increasing by 2 inches every hour.
Write an inequality to determine when the water in Tank A will be deeper than the water in Tank B.

Define the variable:

Write the inequality:

variable: number of hours

inequality (unsimplified): 4x+3 > 2x+10

inequality (simplified): x > 3.5

at least 4 hours

Step-by-step explanation:

we can use mx+b to solve this. m will be the rate at which the water level rises and b will be your stating point. x defines the hour; this is your varible as it can change

Tank A: 4x+3

Tank B: 2x+10

since we want to find when tank a will have be deeper than tank b, we set the inequality to solve for greater than tank a: 4x+3 > 2x+10

subtract 3 to both sides: 4x > 2x + 7

subtract 2x to both sides: 2x > 7

divide both sides by 2: x > 3.5

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3