Markus jogs 4 mi around a track at an average rate of r mi/h Then he cools down by walking 1 mi at a rate 3 mi/h slower. His whole workout lasts 1 h. At what rates did Markus jog and walk?
To solve this problem, we can set up a system of equations using the given information.
Let's call the rate at which Markus jogs "r" mi/h, the rate at which Markus walks during his cool down "w" mi/h, and the time it takes Markus to jog the 4 miles "t" hours.
Based on the information given, we can write the following equations:
Equation 1: Distance = Speed × Time
For Markus's jogging: 4 miles = r mi/h × t hours
For Markus's cool down: 1 mile = (r - 3) mi/h × (1 - t) hours
Equation 2: Total time = Jogging time + Cool down time
1 hour = t hours + (1 - t) hours
Now, we can solve the system of equations to find the values of "r" and "w".
From Equation 1:
4 miles = r mi/h × t hours (Equation 1.1)
1 mile = (r - 3) mi/h × (1 - t) hours (Equation 1.2)
From Equation 2:
1 hour = t hours + (1 - t) hours (Equation 2.1)
First, we'll solve Equation 2.1 for "t":
1 hour = t + 1 - t
1 hour = 1
Since both sides are equal, this equation holds true.
Now, substituting t = 1 into Equation 1.1:
4 miles = r mi/h × (1 hour)
4 miles = r mi/h
r = 4 mi/h
Now, substituting t = 1 into Equation 1.2:
1 mile = (r - 3) mi/h × (1 - 1 hour)
1 mile = (4 mi/h - 3 mi/h) × 0 hour
1 mile = 1 mi/h × 0 hour
1 mile = 0 mi
Since both sides are not equal, this equation does not hold true.
Therefore, there is no solution for "w" (the rate at which Markus walks during his cool down). It appears that there might be an error in the given information or a contradiction in the problem statement.