Acontainer has 130 gallons of water and is being filled at a rate of 1/4 gallon each second. another container has 200 gallons of water and is draining at a rate of 1/3 gallon each second. when will the 2 containers have the same amount of water?

120 seconds

Step-by-step explanation:

To solve this question you have to make equation of both gallon.

Gallon 1 have 130 gallons of water at the start and filled by 1/4 gallon each second. If x equal to the time in seconds, the equation of gallon 1 volume will be:

g1= 130+ 1/4x

Gallon 1 have 200 gallons of water at the start and drained by 1/ 3  gallon each second,  the equation of gallon 2 volume  :  

g2= 200- 1/3x

When gallon 1 volume equal to gallon 2, it mean g1=g2

g1= g2

130+ 1/4x  =  200- 1/3x  

130- 200= -1/3x -1/4x

-70= - 4/12x - 3/12x

-7/12x= -70

7/12x= 70

x= 70*12/7

x= 120

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0