We want to find the motion equation for the two horses and then use these equations to find how far would run each horse in 12 minutes.
The motion equations are:
- For horse A: y = (1/4) mi/min*x
- For horse B: y = (2/5) mi/min*x
And in 12 minutes horse A moves 3 miles while horse B moves 4.8 miles
Finding the equations:
We can see that both equations pass through the point (0, 0), thus both equations are proportional equations of the form:
y = k*x
Then to get the equations we just need one point on each line, for example for horse A we can use the point (8 min, 2 mi)
Replacing that in the general equation we get:
2 mi = k*8min
Now we can solve that for k
(2 mi)/(8 min) = k
(1/4) mi/min = k
Notice that this is a speed.
For horse B we can use the point (5 min, 2 mi), in the same way than above we will get:
2 mi = k*5 min
(2mi/ 5 min) = k
(2/5) mi/min = k
Then the two equations are:
- For horse A: y = (1/4) mi/min*x
- For horse B: y = (2/5) mi/min*x
Evaluating the equations
Now we want to see how far would each horse run in 12 minutes, we get this by evaluating bot equations in x = 12 min
For horse A we get:
y = (1/4) mi/min*12min = 3mi
For hose B we get:
y = (2/5) mi/min*12min = 4.8 mi
If you want to learn more about proportional relations, you can read:
https://brainly.com/question/12242745
