On Friday, Kaitlyn went to the park to work out. She started with a slow jog at a constant rate for five minutes. She then increased her speed to a faster, constant pace for seven minutes. She took a three-minute break, then ran for another 7.5 minutes at a constant pace to finish her two-mile run. She rested for the remainder of the time. During what domain interval will she reach 1.25 miles?
(1 point)
Responses
5≤s<12
5 less-than-or-equal-to s less than 12
22.5≤s≤25
22.5 less-than-or-equal-to s less-than-or-equal-to 25
12≤s≤15
12 less-than-or-equal-to s less-than-or-equal-to 15
15≤s≤22.5
15 less-than-or-equal-to s less-than-or-equal-to 22.5
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To determine the domain interval during which Kaitlyn will reach 1.25 miles, we need to add up the amount of time she spends running at each pace until she reaches that distance.
Kaitlyn initially jogs for 5 minutes at a constant rate. This means that after 5 minutes, she has covered a distance of:
1 mile/5 minutes = 0.2 miles/minute
Next, she runs at a faster pace for 7 minutes. Since she has already covered 1 mile, she needs to run for an additional:
1.25 miles - 1 mile = 0.25 miles
Using the formula distance = rate * time, we can calculate her faster pace:
0.25 miles/7 minutes ≈ 0.0357 miles/minute
Therefore, the total rate at which Kaitlyn covers distance during the interval where she reaches 1.25 miles is approximately:
0.2 miles/minute + 0.0357 miles/minute = 0.2357 miles/minute
To determine the time it takes to reach 1.25 miles using this rate, we can use the formula:
time = distance / rate
time = 1.25 miles / 0.2357 miles/minute ≈ 5.297 minutes
Therefore, Kaitlyn will reach 1.25 miles during the interval:
5 minutes ≤ s < 5.297 minutes
or in interval notation:
5 ≤ s < 5.297
Thus, the correct response is:
5 ≤ s < 12