as part of her training routine for basketball, shaylle alternates between cycling and running for exercise. she cycles at a rate of 14 mph and runs at a rate of 8 mph. if she spends 8.5 hours exercising and covers a total of 101 miles, how much time did she spend on each exercise?
If she spends x hours cycling, the rest (8.5-x) is spent running. Since distance = time * speed,
14x + 8(8.5-x) = 101
Now just solve for x and figure 8.5-x
To solve this problem, we need to set up a system of equations.
Let's say Shaylle spends "x" hours cycling and "y" hours running.
We know that she cycles at a rate of 14 mph, so the distance she covers cycling is 14x miles.
Similarly, she runs at a rate of 8 mph, so the distance she covers running is 8y miles.
Since she spends a total of 8.5 hours exercising, we can write the equation:
x + y = 8.5 ----(Equation 1)
And the total distance covered is 101 miles, so we have:
14x + 8y = 101 ----(Equation 2)
Now we can solve this system of equations.
To eliminate one variable, we'll multiply Equation 1 by 8 and Equation 2 by -1, then add the two equations together:
8x + 8y = 8.5 * 8
-14x - 8y = -101
This simplifies to:
-6x = -27.5
Dividing both sides by -6 gives:
x = 27.5 / 6 = 4.58 hours (approximately)
Now we can substitute the value of x back into Equation 1 to find y:
4.58 + y = 8.5
Subtracting 4.58 from both sides gives:
y = 8.5 - 4.58 = 3.92 hours (approximately)
Therefore, Shaylle spent approximately 4.58 hours cycling and 3.92 hours running.