Asked by Nissan GT-R R35 Nismo
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 2-mile run. She rested for the remainder of the time.
During what domain interval will she reach 1.5 miles?
22.5 ≤ s ≤ 25
12 ≤ s ≤ 15
15 ≤ s ≤ 22.5
5 ≤ s ≤ 12
All Answers 1
Answered by
GPT-5 mini
AI
15 ≤ s ≤ 22.5
Reason: Let the slow pace be r1 and the faster pace (used for the 7- and 7.5-minute runs) be r2. Then
5r1 + 14.5r2 = 2.
After 12 minutes she has gone 5r1 + 7r2 = 2 − 7.5r2. If 5r1 + 7r2 ≥ 1.5 then r1 ≥ 0.2067, but r1 must be less than r2, which (from 5r1 + 14.5r2 = 2) forces r1 < 0.1026 — a contradiction. Thus she cannot reach 1.5 miles by 12 minutes or earlier, nor during the break (12–15). She therefore reaches 1.5 miles during the final 7.5-minute run, i.e. for 15 ≤ s ≤ 22.5.
Reason: Let the slow pace be r1 and the faster pace (used for the 7- and 7.5-minute runs) be r2. Then
5r1 + 14.5r2 = 2.
After 12 minutes she has gone 5r1 + 7r2 = 2 − 7.5r2. If 5r1 + 7r2 ≥ 1.5 then r1 ≥ 0.2067, but r1 must be less than r2, which (from 5r1 + 14.5r2 = 2) forces r1 < 0.1026 — a contradiction. Thus she cannot reach 1.5 miles by 12 minutes or earlier, nor during the break (12–15). She therefore reaches 1.5 miles during the final 7.5-minute run, i.e. for 15 ≤ s ≤ 22.5.
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