(a) For each pool, an expression for the amount of water in the pool after x minutes include;
Amount of water in the first pool (in liters) = 3650 - 27x.
Amount of water in the second pool (in liters) = 4166 - 39x.
(b) An equation to show when the two pools would have the same amount of water is 3650 - 27x = 4166 - 39x.
In Mathematics and Geometry, the slope-intercept form of the equation of a straight line refers to the general equation of a linear function and it is represented by this mathematical equation;
y = mx + b
Where:
- m represents the slope or rate of change.
- x and y are the points.
- b represents the y-intercept or initial value.
Part a.
Since the first pool had 3650 liters of water at start and water is being drained from it at a rate of 27 liters per minute, it means that its y-intercept is 3650 and its slope is -27 because the water is decreasing. Hence, an expression for the amount of water in the first pool (in liters) is given by;
3650 - 27x.
Also, the second pool had 4166 liters of water at start and water is being drained from it at a rate of 39 liters per minute, it means that its y-intercept is 4166 and its slope is -39 because the water is decreasing. Hence, an expression for the amount of water in the second pool (in liters) is given by;
4166 - 39x
Part b.
An equation to show when the two pools would have the same amount of water can be written by equating the two expressions above as follows;
3650 - 27x = 4166 - 39x.
39x - 27x = 4166 - 3650
12x = 516
x = 516/12
x = 43 minutes.
In conclusion, the two pools would have the same amount of water in 43 minutes.