As part of her training routine for basketball, Shaylle alternates between cycling and running for exercise. She cycles at a rate of 16 mph and runs at a rate of 8 mph. If she spends 8.5 hours exercising and covers a total of 112 miles, how much time did she spend on each exercise?
c+r = 8.5
16c+8r = 112
Now just solve for c and r.
To find out how much time Shaylle spent on each exercise, we can set up a system of equations based on the given information.
Let's call the time she spent cycling "c" and the time she spent running "r".
From the given information, we know that the total time she spent exercising is 8.5 hours, so we can write the equation:
c + r = 8.5 (equation 1)
We also know the distances covered during each exercise. The distance covered while cycling is 16 mph times the time spent cycling (16c), and the distance covered while running is 8 mph times the time spent running (8r). The total distance covered is 112 miles, so we can write the equation:
16c + 8r = 112 (equation 2)
Now we have two equations with two variables (c and r). We can solve this system of equations to find the values of c and r.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
From equation 1, we can express c in terms of r:
c = 8.5 - r
We can substitute this expression for c in equation 2:
16(8.5 - r) + 8r = 112
Now we can simplify and solve for r:
136 - 16r + 8r = 112
-8r = 112 - 136
-8r = -24
r = (-24)/(-8)
r = 3
Now that we have the value of r, we can substitute it back into equation 1 to find the value of c:
c + 3 = 8.5
c = 8.5 - 3
c = 5.5
Therefore, Shaylle spent 5.5 hours cycling and 3 hours running.