Aquarium 1 contains 4.6 gallons of water. Daniel will begin filling Aquarium 1 at a rate of 1.2 gallons per minute. Aquarium 2 contains 54.6 gallons. Janet will begin draining Aquarium 2 at a rate of 0.8 gallons per minute. After how many minutes will both aquariums contain the same amount of water?

25 minutes

Explanation:

Let us analyse the problem carefully;

In aquarium 1, the rate volume of water is increasing at a rate of 1.2 gallons per minute. If we are to plot this into a straight line graph, we will plot the volume at each time (y) against the time (x) with the initial volume water in each aquarium as the constant in each case. The rate of increase or decrease of water is the slope of the graph (m). Recall that the equation of a straight line graph is y=mx + c

For Aquarium 1

y= 1.2x + 4.6   Equation 1

For Aquarium 2

y= -0.8x + 54.6        Equation 2

For aquarium 2, since the volume is decreasing, the slope is negative      

The time at which both aquariums will contain the same volume of water is obtained by equating equations 1 and 2 above;

1.2x + 4.6= -0.8x + 54.6

1.2x + 0.8x = 54.6 - 4.6

2x = 50

x = 50/2

x= 25 minutes