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Floyd started at one end of a trail at 8:07 a.m. and hiked the entire [#permalink]
rsvp wrote:
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


Given:
1. 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.
2. 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.
3. 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.

Asked: 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?

Attachment:
Screenshot 2020-05-27 at 10.42.53 PM.png
Screenshot 2020-05-27 at 10.42.53 PM.png [ 22.1 KiB | Viewed 4487 times ]


Floyd and Connie were together for = 9:47 - 8:30 = 1:17 hrs
Connie and Karen were together for = 10:30 - 10:00 = 0:30 hrs
Floyd and Karen were never together.

Approximately percent of the 4-hour period from 8:00 a.m. to noon when at least two of the three hikers on the trail = 1:47/4:00 = 44.58% ~ 45%

IMO B

Originally posted by Kinshook on 27 May 2020, 10:14.
Last edited by Kinshook on 27 May 2020, 10:20, edited 1 time in total.
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Re: Floyd started at one end of a trail at 8:07 a.m. and hiked the entire [#permalink]
Hi nick1816

Karen is on trail from 10:00 to 11:15 hrs (75 mins)


nick1816 wrote:
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 11:30.

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 wrote:
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
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Re: Floyd started at one end of a trail at 8:07 a.m. and hiked the entire [#permalink]
That was a typo. Edited!


Kinshook wrote:
Hi nick1816

Karen is on trail from 10:00 to 11:15 hrs (75 mins)


nick1816 wrote:
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 11:30.

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 wrote:
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


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Re: Floyd started at one end of a trail at 8:07 a.m. and hiked the entire [#permalink]
Expert Reply
rsvp wrote:
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%



It takes Floyd 5/3 hours or 1 hour and 40 minutes to finish the trail. So he reaches the other end of the trail at 8:07 am + 1 hr 40 min = 9:47 am.

Similarly, it takes Connie 5/2.5 = 2 hours to finish the same trail. So she reaches the other end of the trail at 8:30 am + 2 hrs = 10:30 am.

Finally, it takes Karen 5/4 hours or 1 hour and 15 minutes to finish the trail. So she reaches the other end of the trail at 10 am + 1 hr 15 min = 11:15 am.

We can see that both Floyd and Connie are on the trail from 8:30 am to 9:47 am (i.e., 1 hour and 17 minutes), and both Connie and Karen are on the trail from 10 am to 10:30 am (i.e., 30 minutes). However, all three hikers are not on the trail simultaneously since Floyd finishes his hike before Karen begins hers. Therefore, for a total of 1 hour and 47 minutes we have at least two of the three hikers on the trail. Since 1 hour and 47 minutes = 107 minutes and 4 hours = 240 minutes, the percent of time we have at least two of the three hikers on the trail is 107/240 = 0.4458 or approximately 45%.

Answer: B
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Re: Floyd started at one end of a trail at 8:07 a.m. and hiked the entire [#permalink]
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