Dudley and Bob monitored the distance their pet turtle could walk in a certain amount of time.Their results are shown in the table.The table of values represents a proportional relationship.
Time(minutes):5,14,19,25
Distance(inches):14.5,40.6,55.1,72.5
A.Define variable for the quantities that are changing in this problem situation.
B.Write an equation for the distance traveled by the turtle based on the number of minutes.
(this is not multiple choice 🧐)
First, can you determine the speed of the turtle in units of inches per minute?
A. The variable for the quantity that is changing in this problem situation is time (minutes) and distance (inches).
B. Let's write an equation for the distance traveled by the turtle based on the number of minutes. We can use the slope-intercept form of a linear equation, y = mx + b, where y represents the distance and x represents the time.
First, let's calculate the slope (m):
slope (m) = (change in y) / (change in x) = (72.5 - 14.5) / (25 - 5) = 58 / 20 = 2.9
Now, we can write the equation:
distance = 2.9 * time + b
To find the value of b (the y-intercept), we can substitute one set of values into the equation. Let's use the first set of values (5 minutes and 14.5 inches):
14.5 = 2.9 * 5 + b
14.5 = 14.5 + b
b = 14.5 - 14.5
b = 0
The equation for the distance traveled by the turtle based on the number of minutes is:
distance = 2.9 * time + 0
Simplifying, we get:
distance = 2.9 * time
A. We can define two variables for the quantities that are changing in this problem situation:
- Let "t" represent the time in minutes.
- Let "d" represent the distance traveled by the turtle in inches.
B. To write an equation for the distance traveled by the turtle based on the number of minutes, we can use the concept of a proportional relationship. In a proportional relationship, the ratio between the two variables remains constant.
From the table of values, we can see that the ratio between the distance traveled and the time in minutes is constant. This ratio is given by:
(distance / time) = constant
Let's calculate the constant using one of the pairs of values from the table, say (5, 14.5):
(14.5 / 5) = 2.9
Now we can write the equation based on this constant:
d = 2.9t
Therefore, the equation for the distance traveled by the turtle based on the number of minutes is d = 2.9t.
To define the variables for the quantities that are changing in this problem situation, let's denote the time in minutes as "t" and the distance in inches as "d".
A. Variables:
- Time (minutes): t
- Distance (inches): d
B. Equation for the distance traveled by the turtle based on the number of minutes:
To determine the equation, we need to establish the relationship between time and distance. From the given table, we can see that as time increases, the distance also increases. This indicates a proportional relationship between time and distance.
To find the equation, we need to determine the constant of proportionality, which is the ratio between the distance and time.
We can do this by taking any of the data points and dividing the distance (d) by the time (t):
For example, let's use the first data point: (t,d) = (5,14.5)
The constant of proportionality is the ratio of the distance to the time: d/t
Using the first data point:
d/t = 14.5/5 = 2.9
Now, we can write the equation for the distance traveled by the turtle based on the number of minutes (t):
d = 2.9t
Therefore, the equation for the distance traveled by the turtle is:
Distance (d) = 2.9 times the Time (t)