Example 3

As a tank of water is drained, 10 L will flow out in the first 30 seconds and then another 10 L will flow out in the next 15 seconds, as illustrated in the graph below.

  • Create a graph representing the situation described. Be sure to plot the amount of water drained versus time and label the graph.
  • Determine the slope for each time interval—the first 30 seconds and then the next 15 seconds.
  • Analyze what is happening during each interval.

Slope for the first 30 seconds.

Slope for the first 30 seconds is 0.33 L/sec.

Slope for the next 15 seconds.

Slope for the next 15 seconds is 0.67 L/sec.

For the second time interval, between 30 s and 45 s, the unit rate is larger and the slope of the graph is steeper. As such, the water flowed out of the tank faster in the second interval.

For further information about problems involving rates see p. 454 to 458 of Principles of Mathematics 11.