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A hiker walking at a constant rate of 4 miles per hour is passed by a
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09 Nov 2010, 07:01
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A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up? A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3
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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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09 Nov 2010, 07:09
anilnandyala wrote: a hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up a 6 2/3 b 15 c 20 d 25 e 26 2/3
i am getting 25 how it is 20 In 1/12 hours (5 minutes) after the hiker is passed by the cyclist the distance between them will comprise \((204)*\frac{1}{12}=\frac{4}{3}\) miles (note that during these 5 minute hiker walks too, so their relative rate is 204 miles per hour). The hiker thus will need \(\frac{\frac{4}{3}}{4}=\frac{1}{3}\) hours, or 20 minutes to catch up. Answer: C.
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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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09 Nov 2010, 08:42
Cyclist travelled for 5 mins (1/12 hours) before stopping.
Distance between Cyclist & hawker= (1/12)*(204) = 4/3 miles.
Hawker should cover this distance with 4 hours/mile = (4/3)/(4/1)= 1/3hour = 20 minutes.
Answer: C



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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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09 Nov 2010, 08:48
cyclist is relatively 4times faster So in 5 minutes, he has taken the lead for 20 minutes relative to the Hiker.
So he has to wait for 20 minutes



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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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09 Nov 2010, 09:16
Hiker's speed : Cyclist's speed = 4 : 20 = 1 : 5 To cover the same distance, Time taken by Hiker : Time taken by Cyclist = 5 : 1 (If distance is same, speed is inversely proportional to time) If cyclist took 5 mins, Hiker will take 25 mins. So she will need another 20 mins. (When cyclist was covering the distance in 5 mins, the Hiker was also walking for those 5 mins)
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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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15 Oct 2013, 20:23
anilnandyala wrote: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 The cyclist is traveling at a pace of 1 mile every 3 minutes. The hiker is traveling at a pace of 1 mile every 15 minutes. The cyclist passes the hiker, and then 5 minutes later stops, so they are \(\frac{5}{3}\) of a mile from the point they passed the hiker. The hiker is \(\frac{1}{3}\)of a mile past the spot where they were passed. \(\frac{5}{3}\)  \(\frac{1}{3}\) = \(\frac{4}{3}\)of a mile, this is how far ahead the cyclist is from the hiker while they wait. since the hiker takes 15 minutes per mile, it will take \(\frac{4}{3}\)*15=\(\frac{60}{3}\)=20 minutes to catch up to the cyclist.



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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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07 Aug 2015, 02:51
walking guy's speed in miles/min=4/60=1/15. guy in the cycle=20/60=1/3. So it will be = 1/31/15=4/3 thats the speed of the cyclist. now how time will it take to cover 4/3 for the walking guy= 4/3/1/15=20



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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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31 Aug 2015, 09:46
According to my understanding, when moving in same direction, time taken to chatch is represented by  Initial Diference Btwn them/ Difference of their speeds. And When in opposite direction, time taken to meet is represented by  Initial difference btwn then/ Sum of their speeds.
Since they are moving in same direction, the equation is (4/3)/16 * 60, (4/3) Distance Btwn them. 16 Diference in their speeds (as they are moving in same direction) 60 converting Hrs into mins. which comes out to be 5.
Can anyone tell where iam going wrong.



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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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29 May 2017, 03:33
anilnandyala wrote: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 1. Let us start at the point when the cyclist and the hiker are together 2. In 5 min, cyclist travels 20/12 miles, whereas the hiker travels 4/12 miles. 3. The hiker has to make up 20/12  4/12 miles which is 4/3 miles. 4. Time to travel 4/3 miles by the hiker is 4/3 /(4) = 4/12 hrs = 20 min.
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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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25 Jun 2017, 12:36
anilnandyala wrote: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 Speed of Hiker = 4m/hr Speed of Cyclist = 20 m/hr Since both are moving in the same direction, the effective speed of the cyclist = 204 = 16 m/hr So with this speed, the cyclist will travel = (16/60)*5 miles in 5 mins = 4/3 miles Hence, Hiker will take = (4/3)/4 hr to travel 4/3 miles at the speed of 4m/hr So, Time required by hiker = 1/3 hr = 20 mins Option C
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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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17 Jul 2017, 11:25
krushna wrote: cyclist is relatively 4times faster So in 5 minutes, he has taken the lead for 20 minutes relative to the Hiker.
So he has to wait for 20 minutes hi how can you say cyclist is 4 times faster while cyclist's mph is 20 and hiker's mph is 4..? we can see he is 5 times faster please make it clear to me.. thanks



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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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17 Jul 2017, 11:48
VeritasPrepKarishma wrote: Hiker's speed : Cyclist's speed = 4 : 20 = 1 : 5 To cover the same distance, Time taken by Hiker : Time taken by Cyclist = 5 : 1
(If distance is same, speed is inversely proportional to time)
If cyclist took 5 mins, Hiker will take 25 mins. So she will need another 20 mins. (When cyclist was covering the distance in 5 mins, the Hiker was also walking for those 5 mins) hi if the hiker were not walking, he would need 25 minutes to cover the distance passed by the cyclist ...? am i right...? thanks in advance ..



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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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17 Jul 2017, 23:46
ssislam wrote: VeritasPrepKarishma wrote: Hiker's speed : Cyclist's speed = 4 : 20 = 1 : 5 To cover the same distance, Time taken by Hiker : Time taken by Cyclist = 5 : 1
(If distance is same, speed is inversely proportional to time)
If cyclist took 5 mins, Hiker will take 25 mins. So she will need another 20 mins. (When cyclist was covering the distance in 5 mins, the Hiker was also walking for those 5 mins) hi if the hiker were not walking, he would need 25 minutes to cover the distance passed by the cyclist ...? am i right...? thanks in advance .. I am not sure what you mean. If the hiker were not walking, how would he catch up to the cyclist?
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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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18 Jul 2017, 22:02
VeritasPrepKarishma wrote: ssislam wrote: VeritasPrepKarishma wrote: Hiker's speed : Cyclist's speed = 4 : 20 = 1 : 5 To cover the same distance, Time taken by Hiker : Time taken by Cyclist = 5 : 1
(If distance is same, speed is inversely proportional to time)
If cyclist took 5 mins, Hiker will take 25 mins. So she will need another 20 mins. (When cyclist was covering the distance in 5 mins, the Hiker was also walking for those 5 mins) hi if the hiker were not walking, he would need 25 minutes to cover the distance passed by the cyclist ...? am i right...? thanks in advance .. I am not sure what you mean. If the hiker were not walking, how would he catch up to the cyclist? hi maybe it is very obvious.... but I wanted to mean, if the hiker stopped walking as early as the cyclist passed him, and the cyclist continued to run his cycle for 5 minutes, then the time required by the hiker to cover the distance passed by the cyclist would be 25 minutes, provided that the hiker starts walking after 5 minutes.... am I right, mam...?



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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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18 Jul 2017, 23:49
ssislam wrote: hi
maybe it is very obvious....
but I wanted to mean, if the hiker stopped walking as early as the cyclist passed him, and the cyclist continued to run his cycle for 5 minutes, then the time required by the hiker to cover the distance passed by the cyclist would be 25 minutes, provided that the hiker starts walking after 5 minutes....
am I right, mam...? Yes, this is correct. He will take 25 mins to cover the distance. If he were not walking for those 5 mins while the cyclist was cycling away, he would take 25 mins to reach the cyclist.
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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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19 Jul 2017, 11:01
anilnandyala wrote: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 Rather than the calculation part, all the difficulties is hidden in this line "the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate" Initially I thought cyclist waited for 5 min, although the meaning is, cyclist stopped and waited after 5 min when he/she crosses the hiker.



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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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20 Jul 2017, 16:50
anilnandyala wrote: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 We are given that a cyclist travels at a rate of 20 mph, passes a hiker, and then stops to wait for the hiker after traveling for 5 minutes. Since 5 minutes = 1/12 hours, the cyclist travels a distance of 20/12 = 5/3 miles. We let the extra time, in hours, of the hiker = t, and then the hiker’s total time is t + 1/12; thus, the distance in miles of the hiker is 4(t + 1/12) = 4t + 1/3. Since the hiker catches the cyclist, we set their distances equal and determine t: 4t + ⅓ = 5/3 4t = 4/3 t = (4/3)/4 = 4/12 = 1/3 hours = 20 minutes Answer: C
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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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29 Sep 2017, 21:40
I approached this by calculating how far ahead of the walker the biker is when he's waiting. This is calculated by:
(Biker Speed  Walker Speed) * Time until biker stops to wait (20  4) * 6 = 16*4 = 80km
Then i calculated how long it would take for the walker to walk this distance. 4*t = 80 t = 20



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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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04 Oct 2018, 15:20
Quote: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. Five minutes after the passing the cyclist stops, while the hiker continues to walk at the hiker´s rate. How many minutes must the cyclist wait until the hiker catches up?
A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3
\(?\,\,\,:\,\,\,{\text{minutes}}\,\,\,\left( {{\text{last}}\,\,{\text{diagram}}} \right)\) Let´s use UNITS CONTROL, one of the most powerful tools of our method! \({\rm{cyclist}}:\,\,\,5\min \,\,\left( {{{20\,\,{\rm{miles}}} \over {60\,\,\min }}\,\matrix{ \nearrow \cr \nearrow \cr } } \right)\,\,\, = {5 \over 3}\,\,{\rm{miles}}\) \({\rm{hiker}}:\,\,\,{5 \over 3}{\rm{miles}}\,\,\left( {{{60\,\,{\rm{min}}} \over {4\,\,{\rm{miles}}}}\,\matrix{ \nearrow \cr \nearrow \cr } } \right)\,\,\, = 25\,\,{\rm{minutes}}\) Obs.: arrows indicate licit converters. \(? = 25  5\left( * \right) = 20\min\) \(\left( * \right)\,\,{\rm{used}}\,\,{\rm{while}}\,\,\left( {{\rm{also}}} \right)\,\,{\rm{cyclist}}\,\,{\rm{was}}\,\,{\rm{moving}}!\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a
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04 Oct 2018, 15:46
anilnandyala wrote: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 We find the distance that the cyclist reached after passing the hiker for 5 minutes 5/60 = 1/12 * 20 = 10/6 = 5/3 The distance the hiker reaches walking for 5 minutes = 5/60 * 4 = 20/60 = 1/3 The difference in distance is 5/3  1/3 = 4/3 The time for the hiker to reach the cyclist = (4/3)/4 = 4/12 = 1/3 * 60 = 20 minutes. This is the same as the time the cyclist has to wait. Answer choice C. Posted from my mobile device




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