A fish tank is being filled with water. The graph below shows the relationship between the amount of water W (in liters) in the tank and the time T (in minutes) since the tank started being filled.
Amount of water (liters)
W102030405060708090100T1234567890
Time (minutes)
(a)Write an equation to represent the relationship between W and T.
(b)Choose the correct statement to represent this relationship.
The fish tank is being filled with 1 liter of water per 10 minutes.
The fish tank is being filled with 20 liters of water per minute.
The fish tank is being filled with 10 liters of water per minute.
The fish tank is being filled with 1 liter of water per 20 minutes.
(a) The equation to represent the relationship between W (amount of water in liters) and T (time in minutes) is:
W = 10T
(b) The correct statement to represent this relationship is:
The fish tank is being filled with 10 liters of water per minute.
(a) To write an equation representing the relationship between W and T, we can look at the graph. From the graph, we can see that for every 10 minutes (T), the amount of water (W) increases by 10 liters. Therefore, the equation can be written as:
W = 10T
(b) The correct statement to represent this relationship is:
The fish tank is being filled with 10 liters of water per minute.
To find the equation representing the relationship between the amount of water W and the time T, we can analyze the given information.
Looking at the graph, we can see that the amount of water W increases by a constant rate over time. This indicates a linear relationship between W and T.
To find the slope of the line (which represents the rate of change), we can choose two points on the line and calculate the change in W divided by the change in T.
Let's choose the points (0, 0) and (10, 20) from the graph.
Change in W = 20 - 0 = 20 liters
Change in T = 10 - 0 = 10 minutes
The slope of the line is given by the ratio of the changes:
Slope = change in W / change in T
Slope = 20 liters / 10 minutes
Slope = 2 liters/minute
So, the equation representing the relationship between W and T is:
W = 2T
Now let's determine which statement, from the given options, represents this relationship accurately.
The fish tank is being filled with 20 liters of water per minute.
This statement correctly represents the relationship between W and T.