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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

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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

The OA is B

Source: Veritas Prep

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swerve 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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Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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swerve 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
(man's rate)/(woman's rate) = (4 mph)/(20 mph) = 1/5.

Between the moment when the woman passes the man and the moment when she stops to wait, the woman and the man each travel for 5 minutes.
During these 5 minutes, the woman travels x miles.
Since the man's rate is 1/5 the woman's rate, the man's time to travel these x miles will be 5 times the woman's time:
5*5 = 25 minutes.
Since the man has already traveled for 5 minutes -- and he needs a total of 25 minutes to travel the x miles traveled by the woman -- the time for the man to catch up = 25-5 = 20 minutes.

The correct answer is B.

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