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

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.

Answer B.

I solved it very traditionally

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

answer : 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.

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

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.

Women travelling 16 miles/hour relative to man moves for 5 minutes and covers a distance of 4/3 miles.

Man covers 4/3 miles @4 miles/hour in 20 minutes

IMO B

Posted from my mobile device

This is a very good example of relative velocity.

Since the Man is walking at a Speed of 4 Miles Per Hour and the Woman is walking at a Speed of 20 Miles Per Hour their Relative Speed becomes 20-4= 16 Miles Per Hour.

"The woman stops to wait for the man 5 minutes after passing him"
The problem says that the Woman walks for 5 Minutes and then stops for the man, hence the distance that the woman has traveled is 16*(5/60)=4/3 Miles.

To know how much time the woman needs to wait we need to calculate how much time will the man take to reach the woman.

The distance between them is 4/3 Miles, we already know the speed of the man, we just need to calculate the time.

D=S*T
4/3=4*T
T=1/3 Hours.

Note that the options are given in minutes hence we'll have to convert this answer to minutes.
1/3 Hours = 20 Minutes.

Hence the answer is B = 20 minutes.

If this answer helped you, a kudos will go a long way.

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

In 60 minutes, the woman pass 16 miles more than the man. So in 5 mins, the women passes 5*16/60 or, 4/3 miles more. The man will take 60/4 * 4/3 = 20 minutes to reach the distance. So, the woman has to wait 20 minutes.

After 5 minutes the distance between the man and woman is:

20(1/12) - 4(1/12) = 20/12 - 4/12 = 16/12 = 4/3 miles

Thus, it takes the man (4/3)/4 = 4/12 = 1/3 hour, or 20 minutes, to catch up with the woman.

Answer: B

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