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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)
12≤t≤15
15≤t≤22.5
5≤t≤12
22.5≤t≤25
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Answer: 15 ≤ t ≤ 22.5.
Reason: The most she could have run by t = 12 is if her slow jog equaled her faster pace; then she would have run 12 of the total 19.5 running minutes, so distance = (12/19.5)·2 = 24/19.5 ≈ 1.2308 < 1.25. With a slower start she covers even less by t = 12, and she doesn't add distance during the 3-minute break (12–15). Thus she must reach 1.25 miles during the final running segment from t = 15 to t = 22.5.
Reason: The most she could have run by t = 12 is if her slow jog equaled her faster pace; then she would have run 12 of the total 19.5 running minutes, so distance = (12/19.5)·2 = 24/19.5 ≈ 1.2308 < 1.25. With a slower start she covers even less by t = 12, and she doesn't add distance during the 3-minute break (12–15). Thus she must reach 1.25 miles during the final running segment from t = 15 to t = 22.5.
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