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# A man walking at a constant rate of 4 miles per hour is pass

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

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18 Sep 2012, 11:43
3
14
00:00

Difficulty:

65% (hard)

Question Stats:

62% (01:42) correct 38% (01:48) wrong based on 403 sessions

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A man walking at a constant rate of 4 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 20 miles per hour. The woman stops to wait for the man 5 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up?

(A) 16 mins
(B) 20 mins
(C) 24 mins
(D) 25 mins
(E) 28 mins

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

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18 Sep 2012, 12:28
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carcass wrote:
A man walking at a constant rate of 4 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 20 miles per hour. The woman stops to wait for the man 5 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up?

(A) 16 mins
(B) 20 mins
(C) 24 mins
(D) 25 mins
(E) 28 mins

The relative speed = 20-4 = 16 miles per hour;

Therefore, in 1/12 hours (5 minutes) the women covers 16*1/12=4/3 miles more than the man.

To cover that distance the man will need (4/3)/4 = 1/3 hours or 20 minutes.

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

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18 Sep 2012, 13:11
R * T = D

Man= 4 m/h
Woman= 20 m/h

Rate at which woman moves ahead of man= 20-4=16 m/h

after passing the man, the woman walks for 5 minutes and then stops: 16 * 5/60 = 4/3 miles. She walks for 4/3 miles.

How long will it take the man to catch up AKA walk 4/3 miles at his rate?
4 * t = 4/3
t=1/3 hours = 20 minutes

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

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18 Sep 2012, 22:30
1
carcass wrote:
A man walking at a constant rate of 4 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 20 miles per hour. The woman stops to wait for the man 5 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up?

(A) 16 mins
(B) 20 mins
(C) 24 mins
(D) 25 mins
(E) 28 mins

Pay attention to the units. The speeds are given in miles per hour, which have to be divide by 60 to find the speeds in miles per minute.
If you have trouble remembering how to apply relative speeds, objects moving in the same direction, opposite direction...just make a drawing.
When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M):

m------M---------------W
w
In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 5*20/60 =5/3 miles and the man walks the distance mM, which is 5*4/60 = 1/3 mile.
The difference of 5/3 - 1/3 =4/3 miles (MW) will be covered by the man in (4/3)/4 = 1/3 of an hour, which is 20 minutes.

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

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04 Feb 2015, 15:04
2

Women takes 60 min to go 20 miles
so for 5 minutes she goes 5/3 miles

Man takes 60 min to go 4 miles
" " 5 min to go 1/3 miles

so distance in five minutes; 5/3 - 1/3 = 4/3 miles min

Man goes 4 miles in 60 minutes
4/3 miles in= (60 x 4) / (4 x 3) = 20 minutes

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

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04 Feb 2015, 20:19
1
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Salvetor wrote:

Women takes 60 min to go 20 miles
so for 5 minutes she goes 5/3 miles

Man takes 60 min to go 4 miles
" " 5 min to go 1/3 miles

so distance in five minutes; 5/3 - 1/3 = 4/3 miles min

Man goes 4 miles in 60 minutes
4/3 miles in= (60 x 4) / (4 x 3) = 20 minutes

Try to solve it using relative speed as well and ensure you are comfortable with the concept. It doesn't matter much in this question but it could make a lot of difference in some cases. If you are not very comfortable with relative speed, check out the concept here:

http://www.veritasprep.com/blog/2012/07 ... elatively/
http://www.veritasprep.com/blog/2012/08 ... -speeding/
http://www.veritasprep.com/blog/2012/08 ... -concepts/
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Re: A man walking at a constant rate of 4 miles per hour is pass  [#permalink]

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27 Feb 2016, 18:17
5 minutes after passing man
woman has traveled 20/12=5/3 mile
man has walked 4/12=1/3 mile
5/3-1/3=4/3 miles between them
4/3 miles/4 mph=1/3 hour=20 minutes for man to catch up
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Re: A man walking at a constant rate of 4 miles per hour is pass  [#permalink]

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21 Nov 2018, 12:17
carcass wrote:
A man walking at a constant rate of 4 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 20 miles per hour. The woman stops to wait for the man 5 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up?

(A) 16 mins
(B) 20 mins
(C) 24 mins
(D) 25 mins
(E) 28 mins

Excellent opportunity for relative velocity (speed) and UNITS CONTROL :

$${{16\,\,{\rm{miles}}} \over {1\,\,{\rm{hour}}}}\,\,\, \cdot \,\,\,\left( {{{1\,\,{\rm{hour}}} \over {\,60\,\,{\rm{minutes}}\,}}} \right)\,\,\, \cdot \,\,\,5\,\,{\rm{minutes}}\,\,\,\,{\rm{ = }}\,\,\,\,{4 \over 3}\,\,{\rm{miles}}\,\,\,\,\,\,\,\left( {{\rm{woman}}\,{\rm{ - }}\,{\rm{man}}\,\,{\rm{distance}}\,{\rm{,}}\,\,{\rm{both}}\,\,{\rm{walking}}\,\,{\rm{during}}\,\,{\rm{5}}\,\,{\rm{minutes}}} \right)$$

$${\rm{only}}\,\,{\rm{man}}\,\,{\rm{walking}}\,\,\,\,:\,\,\,\,\,?\,\,\, = \,\,\,\,{4 \over 3}\,\,{\rm{miles}}\,\,\, \cdot \,\,\,\left( {{{1\,\,{\rm{hour}}} \over {\,4\,\,{\rm{miles}}\,}}} \right)\,\,\,\,\, = \,\,\,\,{1 \over 3}\,\,\,{\rm{hour}}\,\,\, = \,\,20\min \,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{B}} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: A man walking at a constant rate of 4 miles per hour is pass &nbs [#permalink] 21 Nov 2018, 12:17
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