Answer: x1 = 251/26, x2 = -111/26
Step-by-step explanation:
Hi!
As you can see in the figure, the point you are looking for is the intersection of two lines.
The intersection point is found solving this system of linear equations (the point must satisfy both equations):
You can solve it, for example, by the method of substitution:
Then plug x1 into equation 2, and solve for x2:
Then you use the value of x2 to get x1:
Let the distance of the first part of the race be x, and that of the second part, 15 - x, then
x/8 + (15 - x)/20 = 1.125
5x + 2(15 - x) = 40 x 1.125
5x + 30 - 2x = 45
3x = 45 - 30 = 15
x = 15/3 = 5
Therefore, the distance of the first part of the race is 5 miles and the time is 5/8 = 0.625 hours or 37.5 minutes
The distance of the second part of the race is 15 - 5 = 10 miles and the time is 1.125 - 0.625 = 0.5 hours or 30 minutes.
Total expenses: $245.00
Total revenue: $479.00
Total profit $234.00
The matrices must be the same size
Good luck
