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26 May 2020, 11:31
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Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
67% (03:26) correct
33%
(03:28)
wrong
based on 538
sessions
History
Date
Time
Result
Not Attempted Yet
Floyd started at one end of a trail at 8:07 a.m. and hiked the entire 5 miles to the other end of the trail at an average rate of 3 miles per hour. Connie started at the same end of the trail at 8:30 a.m. and hiked the entire length of the trail at an average rate of 2.5 miles per hour. Finally, Karen started her hike in the same place at 10:00 a.m. and hiked the entire length of the trail at an average rate of 4 miles per hour. During approximately what percent of the 4-hour period from 8:00 a.m. to noon were at least two of the three hikers on the trail?
(A) 34%
(B) 45%
(C) 55%
(D) 59%
(E) 68%
Source: Advanced Quant Manhattan Prep 2020
(A) 34%
(B) 45%
(C) 55%
(D) 59%
(E) 68%
Source: Advanced Quant Manhattan Prep 2020
26 May 2020, 23:01
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Well, it took me 3 minutes and 20 seconds to get the right answer.
I do not see a shortcut to this question. So have to perform the following calculation.
(1) 8:07 starts. Duration:1 hour and 40 minutes. So 8:07-9:47
(2) 8:30 starts. Duration: 2 hours. So: 8:30-10:30
(3) 10:00 starts. Duration is over 1 hour. That is enough.
at least two of the three hikers on the trail
8:30-9:47 => Almost 75 minutes
10:00-10:30 => 30 minutes.
75+30 = 105
105/240 = 52.5/120 So, (B) it is.
I do not see a shortcut to this question. So have to perform the following calculation.
(1) 8:07 starts. Duration:1 hour and 40 minutes. So 8:07-9:47
(2) 8:30 starts. Duration: 2 hours. So: 8:30-10:30
(3) 10:00 starts. Duration is over 1 hour. That is enough.
at least two of the three hikers on the trail
8:30-9:47 => Almost 75 minutes
10:00-10:30 => 30 minutes.
75+30 = 105
105/240 = 52.5/120 So, (B) it is.
General Discussion
26 May 2020, 16:03
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Floyd takes \(\frac{5}{3}*60 = 100\) mins to cross the trail. So he is on the trail from 8:07 to 9:47.
Connie takes \(\frac{5}{2.5}*60 = 120\) mins to cross the trail. So he is on the trail from 8:30 to 10:30.
Karen takes \(\frac{5}{4}*60 = 75\) mins to cross the trail. So she is on the trail from 10:00 to 11:15.
From 8-8:30, none or only Floyd is on the trail. (30 minutes)
From 9:47-10:00, only Connie is on the trail. ( 13 minutes)
From 10:30- 12:00, none or only Karen is on the trail. (1 hour and 30 minutes)
Total duration from 8:00 a.m. to noon when at least two of the three hikers were on the trail = 240-30-13-90= 107 minutes
40% of 240 = 96 and 50% of 240 = 120
B
Connie takes \(\frac{5}{2.5}*60 = 120\) mins to cross the trail. So he is on the trail from 8:30 to 10:30.
Karen takes \(\frac{5}{4}*60 = 75\) mins to cross the trail. So she is on the trail from 10:00 to 11:15.
From 8-8:30, none or only Floyd is on the trail. (30 minutes)
From 9:47-10:00, only Connie is on the trail. ( 13 minutes)
From 10:30- 12:00, none or only Karen is on the trail. (1 hour and 30 minutes)
Total duration from 8:00 a.m. to noon when at least two of the three hikers were on the trail = 240-30-13-90= 107 minutes
40% of 240 = 96 and 50% of 240 = 120
B
rsvp
