As part of her training routine for basketball, Shaylle alternates between cycling and running for exercise. She cycles at a rate of 10 mph and runs at a rate of 6 mph. If she spends 2.5 hours exercising and covers a total of 21 miles, how much time did she spend on each exercise?
time spent cyling --- x hrs
times spent running --- (2.5 - x) hrs
10x + 6(2.5-x) = 21
carry on
To determine how much time Shaylle spent on each exercise, let's assign variables to unknown values:
Let x represent the time in hours Shaylle spent cycling.
Let y represent the time in hours Shaylle spent running.
We can set up a system of two equations based on the given information:
Equation 1: Shaylle cycles at a rate of 10 mph and covers a distance of 21 miles, so we have the equation:
10x + 6y = 21 (since distance = rate x time)
Equation 2: Shaylle spends a total of 2.5 hours exercising, so we have the equation:
x + y = 2.5 (since total time = time cycling + time running)
We now have a system of two equations with two variables. We can use substitution or elimination method to solve the system.
Using substitution method:
From equation 2, we can express x in terms of y:
x = 2.5 - y
Substituting this value of x in equation 1:
10(2.5 - y) + 6y = 21
25 - 10y + 6y = 21
25 - 4y = 21
-4y = 21 - 25
-4y = -4
y = 1
Substituting the value of y into equation 2:
x + 1 = 2.5
x = 2.5 - 1
x = 1.5
Therefore, Shaylle spent 1.5 hours cycling and 1 hour running.