Cheryl does a 2 mile warm up trail run at one rate for half of her workout. In the same amount of time she runs an additional 3 miles at a rate that is 2 mph faster. Find Cheryl's rate for her 2 mile warm-up run and for the 3 mile portion of her run.
Rate no. 1 = r mi/h.
Rate no. 2 = r+2 mi/h.
r*t = 2, t = 2/r.
(r+2)*t = 3
(r+2)2/r = 3,
2 + 4/r = 3, 4/r = 1, r = 4 mi/h.
(r+2) = 4+2 = 6 mi/h.
To find Cheryl's rates for her 2-mile warm-up run and the 3-mile portion of her run, we can use the formula:
Rate = Distance / Time
Let's calculate the time Cheryl takes for her 2-mile warm-up run and the 3-mile portion of her run.
For the 2-mile warm-up run, we know that Cheryl runs at a constant rate for half of her workout, which means she spends the same amount of time on the warm-up run as she does on the 3-mile portion of her run. Let's call this time "t."
For the 2-mile warm-up run:
Distance = 2 miles
Time = t
Using the Rate formula, we have:
Rate for warm-up run = Distance / Time
Rate for warm-up run = 2 miles / t
For the 3-mile portion of her run:
Distance = 3 miles
Time = t (since she spends the same amount of time on the warm-up run as the 3-mile portion)
But, in the additional 3-mile portion, Cheryl runs at a rate that is 2 mph faster. Therefore, her speed for the 3-mile portion will be (Rate for warm-up run + 2 mph).
Rate for 3-mile portion = Rate for warm-up run + 2 mph
Rate for 3-mile portion = (2 miles / t) + 2 mph
So Cheryl's rate for her 2-mile warm-up run is 2 miles divided by "t," and her rate for the 3-mile portion is the rate for the warm-up run plus 2 mph.
To find specific values for Cheryl's rates, we would need more information about the total time it takes for her workout or any additional constraints.