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?
It will do you no good to keep posting the same question every minute or two!
That said, try this:
Since time = distance/speed,
4/r + 1/(r-3) = 1
r = 6
Let's break down the problem step by step to find the rates at which Markus jogged and walked.
Step 1: Define the variables
Let's denote the rate at which Markus jogged as "r" mi/h. We need to find this value.
We're also given that the rate at which he walked during his cool-down was 3 mi/h slower, so we can express his walking rate as (r - 3) mi/h.
Step 2: Calculate the time spent jogging and walking
During his jog, Markus covers a distance of 4 miles. The time it takes to jog this distance can be calculated using the formula: Time = Distance / Rate.
Therefore, the time Markus spends jogging is 4 miles / r mi/h = 4/r hours.
During his cool-down walk, Markus covers a distance of 1 mile. The time taken to complete this distance can be calculated in a similar way: Time = Distance / Rate.
So, the time Markus spends walking is 1 mile / (r - 3) mi/h = 1/(r - 3) hours.
Step 3: Calculate the total time
We know from the problem that Markus's entire workout lasted 1 hour. Therefore, the time spent jogging plus the time spent walking should equal 1 hour.
4/r + 1/(r - 3) = 1
Step 4: Solve the equation
To solve the equation, we'll multiply through by the product of the denominators (r(r - 3)) to clear out the fractions.
4(r - 3) + r = r(r - 3)
Next, distribute the 4 on the left side:
4r - 12 + r = r^2 - 3r
Simplify and rearrange the equation to find the quadratic form:
r^2 - 6r + 12 = 0
Step 5: Solve the quadratic equation
Since the quadratic equation doesn't factor easily, we can use the quadratic formula to find the values of "r."
The quadratic formula is: r = (-b ± √(b^2 - 4ac)) / 2a
From the quadratic equation, a = 1, b = -6, and c = 12.
Substituting these values into the quadratic formula:
r = (-(-6) ± √((-6)^2 - 4(1)(12))) / (2(1))
= (6 ± √(36 - 48)) / 2
= (6 ± √(-12)) / 2
Since the square root of a negative number is not a real number, there are no real solutions for the quadratic equation. This means there is no real value for "r" that satisfies the given conditions.
Therefore, it is not possible to determine the rates at which Markus jogged and walked based on the provided information.