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A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]

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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 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 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 \((20-4)*\frac{1}{12}=\frac{4}{3}\) miles (note that during these 5 minute hiker walks too, so their relative rate is 20-4 miles per hour). The hiker thus will need \(\frac{\frac{4}{3}}{4}=\frac{1}{3}\) hours, or 20 minutes to catch up.

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 pa [#permalink]

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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.

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]

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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 = 1/3-1/15=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

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]

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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.

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 pa [#permalink]

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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 = 20-4 = 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

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]

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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...?

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 pa [#permalink]

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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....

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 pa [#permalink]

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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.

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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