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21 Jul 2026, 12:25
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
100% (04:39) correct
0% (00:00) wrong based on 1 sessions
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The distance from Karen' s home to an office is 98.4 miles along a certain route. Along the route, a rest stop is located 83.8 miles from her home and a police car is always within 0.5 mile of the rest stop. Along the route, less than 0.5 mile before the office, Karen' s car broke down. Which of the following values could be the distance, in miles, along the route between Karen' s car and the police car?
Indicate all such values.
13.0
13.5
14.0
14.5
15.0
15.5
16.0
16.5
I am having a hard time finding out the maximum and minimum point in this question
21 Jul 2026, 12:27
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Help please
03 Aug 2026, 07:10
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Explanation
Where is the police car?
The rest stop is 83.8 miles from Karen's home. The police car is always within 0.5 mile of the rest stop, so its location is
\(83.3≤P≤84.3.\)
Where is Karen's car?
The office is 98.4 miles from home. Her car broke down less than 0.5 mile before the office, so her location is
\(97.9<K<98.4.\)
Possible distances between them
Since Karen's car is farther along the route,
distance=\(K-P.\)
The smallest possible distance occurs when:
Karen is as close as possible to the rest stop: K--->97.9 (but not equal), Police is as far forward as possible: P=84.3.
So the distance is
97.9−84.3=13.6,
but since \(K>97.9,\) the distance is actually \(>13.6.\)
The largest possible distance occurs when:
Karen is at the office: K=98.4, Police is as far back as possible: P=83.3.
So the maximum distance is
98.4-83.3=15.1.
Thus the possible distances satisfy
13.6<distance≤15.1.
Check the answer choices
14.0, 14.5, 15.0 are correct.
Where is the police car?
The rest stop is 83.8 miles from Karen's home. The police car is always within 0.5 mile of the rest stop, so its location is
\(83.3≤P≤84.3.\)
Where is Karen's car?
The office is 98.4 miles from home. Her car broke down less than 0.5 mile before the office, so her location is
\(97.9<K<98.4.\)
Possible distances between them
Since Karen's car is farther along the route,
distance=\(K-P.\)
The smallest possible distance occurs when:
Karen is as close as possible to the rest stop: K--->97.9 (but not equal), Police is as far forward as possible: P=84.3.
So the distance is
97.9−84.3=13.6,
but since \(K>97.9,\) the distance is actually \(>13.6.\)
The largest possible distance occurs when:
Karen is at the office: K=98.4, Police is as far back as possible: P=83.3.
So the maximum distance is
98.4-83.3=15.1.
Thus the possible distances satisfy
13.6<distance≤15.1.
Check the answer choices
14.0, 14.5, 15.0 are correct.
