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 6.5 hours exercising and covers a total of 85 miles, how much time did she spend on each exercise?
let her distance covered cycling be x miles
let her distance covered running be 85-x miles
time cycling = x/14
time running = (85-x)/8
x/14 + (85-x)/8 = 6.5
multiply by 56
4x + 7(85-x) = 364
4x + 595 - 7x = 364
-3x = -231
x = 77
so she cycled 77 miles
and ran 8 miles
time cycling = 77/14 = 5.5 hrs
time running = 8/8 = 1 hour
total time = 6.5 hrs , checks out!
Let's denote the time Shaylle spent cycling as "x" and the time she spent running as "y".
We are given the following information:
- Shaylle cycles at a rate of 14 mph.
- Shaylle runs at a rate of 8 mph.
- Shaylle spends 6.5 hours exercising in total.
- Shaylle covers a total distance of 85 miles.
Based on the above information, we can create the following equations:
Equation 1: x + y = 6.5 (since the total time spent cycling and running is 6.5 hours)
Equation 2: 14x + 8y = 85 (since the total distance covered during cycling and running is 85 miles)
To solve this system of equations, we can use the method of substitution. From Equation 1, we can isolate one variable in terms of the other.
Let's solve Equation 1 for x:
x = 6.5 - y
Now, substitute this value of x in Equation 2:
14(6.5 - y) + 8y = 85
Simplify the equation:
91 - 14y + 8y = 85
-6y = -6
y = 1
Now, substitute the value of y back into Equation 1 to find x:
x = 6.5 - y
x = 6.5 - 1
x = 5.5
Therefore, Shaylle spent 5.5 hours cycling and 1 hour running.
To solve this problem, we can set up a system of equations.
Let's assume Shaylle spent x hours cycling and y hours running.
From the given information, we know that her cycling speed is 14 mph, so the distance she covered while cycling is 14x miles.
Similarly, her running speed is 8 mph, so the distance she covered while running is 8y miles.
We also know that she spent a total of 6.5 hours exercising, so we have the equation:
x + y = 6.5 (equation 1)
In addition, the total distance she covered from cycling and running is 85 miles, so we have the equation:
14x + 8y = 85 (equation 2)
We now have a system of two equations with two variables. We can solve it using different methods, such as substitution or elimination.
Let's solve it using the substitution method.
Rearrange equation 1 to solve for x:
x = 6.5 - y
Now substitute this value of x into equation 2:
14(6.5 - y) + 8y = 85
91 - 14y + 8y = 85
-6y = -6
y = 1
Substitute the value of y back into equation 1 to solve for x:
x + 1 = 6.5
x = 5.5
Therefore, Shaylle spent 5.5 hours cycling and 1 hour running in her training routine for basketball.