Let x represent the time in minutes the biker travels, and let y represent the distance, in miles, the biker travels. The relationship between the quantities is linear, as shown in the graph.
We can use two points on the graph to find the equation of the line: (2, just above 0.5) and (5, between 1.5 and 2). Let's estimate the distance at these points to be 0.6 miles and 1.7 miles, respectively.
First, let's find the slope (m) of the line:
m = (y2 - y1) / (x2 - x1) = (1.7 - 0.6) / (5 - 2) = 1.1 / 3 = 0.3667
Now let's find the y-intercept (b) of the line:
y = mx + b
Since we know one point on the line (2, 0.6), we can substitute it into the equation to find the y-intercept:
0.6 = 0.3667(2) + b
0.6 = 0.7334 + b
b = -0.1334
So the equation representing the relationship between the quantities is:
y = 0.3667x - 0.1334
To find how far the biker would travel in 20 minutes, substitute 20 for x:
y = 0.3667(20) - 0.1334
y = 7.334 - 0.1334
y ≈ 7.2 miles
If the biker traveled 48 miles, we can use the equation to find out how many minutes he biked. Substitute 48 for y and solve for x:
48 = 0.3667x - 0.1334
48.1334 = 0.3667x
x ≈ 131.3 minutes
The biker would travel about 7.2 miles in 20 minutes, and if he traveled 48 miles, he biked for about 131.3 minutes.