Question

Two pools are being drained. To start, the first pool had 3650 liters of water and the second pool had 4166 liters of water. Water is being drained from the first pool at a rate of 27 liters per minute. Water is being drained from the second pool at a rate of 39 liters per minute. Let x be the number of minutes water has been drained.

(a) For each pool, write an expression for the amount of water in the pool after x minutes.

Amount of water in the first pool (in liters) = 3650 - 27x
Amount of water in the second pool (in liters) = 4166 - 39x

(b) Write an equation to show when the two pools would have the same amount of water."

(a) 3650 - 27x = 4166 - 39x
(b) 3650 + 27x = 4166 + 39x
(c) 3650 - 39x = 4166 + 27x
(d) 3650 + 39x = 4166 - 27x

Answer 1

To determine when two draining pools will have the same amount of water, we set up and solve the equation 3650 - 27x = 4166 - 39x where x is the number of minutes elapsed.

Step-by-step explanation:

The question involves the creation of algebraic expressions and the setting up of an equation to determine when the water levels in two pools will be equal. To answer part (a) of the question, we create expressions to represent the amount of water remaining in each pool after x minutes of draining. For the first pool, the expression is 3650 - 27x and for the second pool, it is 4166 - 39x.

To find when the pools will have the same amount of water, as described in part (b), we need to set these expressions equal to each other resulting in the equation 3650 - 27x = 4166 - 39x. By solving this equation, we can determine the exact point in time, in minutes, at which both pools will have the same amount of water.