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# A hiker walking at a constant rate of 4 miles per hour is passed by a

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

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09 Nov 2010, 06:01
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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  [#permalink]

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09 Nov 2010, 06:09
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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 $$(20-4)*\frac{1}{12}=\frac{4}{3}$$ 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.

Answer: C.
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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a  [#permalink]

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09 Nov 2010, 07:42
Cyclist travelled for 5 mins (1/12 hours) before stopping.

Distance between Cyclist & hawker= (1/12)*(20-4) = 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  [#permalink]

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09 Nov 2010, 07:48
4
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  [#permalink]

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09 Nov 2010, 08:16
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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  [#permalink]

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15 Oct 2013, 19:23
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  [#permalink]

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07 Aug 2015, 01:51
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
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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a  [#permalink]

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31 Aug 2015, 08:46
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  [#permalink]

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29 May 2017, 02:33
2
1
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  [#permalink]

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25 Jun 2017, 11:36
1
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

Option C
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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a  [#permalink]

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17 Jul 2017, 10:25
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  [#permalink]

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17 Jul 2017, 10:48
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  [#permalink]

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17 Jul 2017, 22:46
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  [#permalink]

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18 Jul 2017, 21:02
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  [#permalink]

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18 Jul 2017, 22:49
1
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  [#permalink]

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19 Jul 2017, 10:01
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  [#permalink]

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20 Jul 2017, 15:50
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  [#permalink]

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29 Sep 2017, 20:40
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  [#permalink]

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04 Oct 2018, 14:20
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  [#permalink]

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04 Oct 2018, 14:46
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.

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Re: A hiker walking at a constant rate of 4 miles per hour is passed by a   [#permalink] 04 Oct 2018, 14:46

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