The graph shows the relationship between the distance a professional biker is traveling and the time in hours.
A graph is shown in the xy-plane. The x-axis is labeled as Time in minutes and the y-axis is labeled as Distance in miles. The values on the x-axis ranges from 0 to 10 in increments of 1 and the values on the y-axis ranges from 0 to 4 in increments of 0 decimal point 5. A line starts from the origin and goes up. Five points are marked on the line. For 1 on the x-axis the value of y is just below 0 decimal point 5 on the line, for 2 on the x-axis the value of y is just above 0 decimal point 5 on the line, for 5 on the x-axis the value of y is between 1 decimal point 5 and 2 on the line, for 8 on the x-axis the value of y is just below 3 on the line, and for 10 on the x-axis the value of y is 3 decimal point 5.
A. Define variables and write an equation to represent the relationship between the quantities.
B. How far would the biker travel in 20 minutes?
C. If the biker traveled 48 miles, how many minutes did he bike? Round to the nearest tenth
A. Let d represent the distance in miles and t represent the time in hours. The equation to represent the relationship between the two quantities is:
d = 0.35t
B. To find out how far the biker would travel in 20 minutes, we need to first convert 20 minutes to hours:
20 minutes ÷ 60 minutes/hour = 0.33 hours
Then, we can substitute 0.33 for t in the equation:
d = 0.35(0.33)
d = 0.1155
Therefore, the biker would travel approximately 0.1155 miles in 20 minutes.
C. To find out how many minutes the biker biked if he traveled 48 miles, we need to rearrange the equation to solve for t:
d = 0.35t
t = d/0.35
t = 48/0.35
t = 137.14
Therefore, the biker biked approximately 137.14 minutes or 2.29 hours (rounded to the nearest tenth).
A. In order to define the variables and write an equation, we need to identify the variables involved in the relationship.
Let's use:
- x to represent the time in minutes,
- y to represent the distance in miles.
The equation that represents the relationship between the quantities can be written as:
y = f(x)
B. To find how far the biker would travel in 20 minutes, we need to use the given graph. Although the graph is labeled in terms of time in minutes, we can still use it by considering time in hours.
Since we know that there are 60 minutes in an hour, 20 minutes is equal to 20/60 = 1/3 hour.
Taking the x-axis as the time and the y-axis as the distance, we can see that the line passes through every point.
Using linear interpolation, we can estimate the corresponding value of y for x = 1/3 hour.
By examining the graph, we can conclude that the y-value for x = 1/3 is approximately 0.25. Therefore, the biker would travel approximately 0.25 miles in 20 minutes.
C. If the biker traveled 48 miles, we need to find the corresponding value of x that satisfies this value.
Using the same approach of linear interpolation on the graph, we can estimate the value of x for y = 48 miles.
Looking at the graph, we can see that the line intersects y = 48 miles somewhere between x = 9 and x = 10.
By visually interpolating, we can estimate that for y = 48 miles, the corresponding value of x is approximately 9.5 hours.
Since we need the number of minutes, we multiply 9.5 by 60 minutes.
Therefore, the biker traveled for approximately 570 minutes when covering a distance of 48 miles.
A. To define the variables and write an equation to represent the relationship between the quantities, we can define the variable "x" as the time in minutes and the variable "y" as the distance in miles.
Based on the information provided, we can observe that the relationship between the time and distance can be represented by a linear equation.
Let's find the equation of the line using the coordinates of two points on the line. We can choose the points (2, 0.5) and (10, 3.5).
Using the slope-intercept form of a linear equation (y = mx + b), we can find the equation as follows:
First, find the slope (m):
m = (3.5 - 0.5) / (10 - 2)
m = 3 / 8
Next, find the y-intercept (b) by substituting the coordinates of one of the points in the equation:
0.5 = (3/8)(2) + b
0.5 = 6/8 + b
0.5 = 3/4 + b
b = 0.5 - 3/4
b = 2/4 - 3/4
b = -1/4
Therefore, the equation representing the relationship between time (x) and distance (y) is:
y = (3/8)x - 1/4
B. To calculate how far the biker would travel in 20 minutes, we substitute x = 20 into the equation:
y = (3/8)(20) - 1/4
y = 15/2 - 1/4
y = 30/4 - 1/4
y = 29/4
y ≈ 7.25
Therefore, the biker would travel approximately 7.25 miles in 20 minutes.
C. To determine how many minutes the biker biked if he traveled 48 miles, we need to solve the equation for x.
48 = (3/8)x - 1/4
To isolate x, we can add 1/4 to both sides:
48 + 1/4 = (3/8)x
Next, we can simplify the equation:
193/4 = (3/8)x
To solve for x, we can multiply both sides by 8/3:
(193/4) * (8/3) = [(3/8)x] * (8/3)
Canceling out common factors:
193 * 8 = x
x = 1544
Therefore, the biker would have biked for approximately 1544 minutes if he traveled 48 miles.