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

Question

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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Official Answer

C

KarishmaB · Accepted Answer

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)

Bunuel · Answer

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.

krushna · Answer

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

SVaidyaraman · Answer

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.

JeffTargetTestPrep · Answer

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

fskilnik · Answer

?\,\,\,:\,\,\,{	ext{minutes}}\,\,\,\left( {{	ext{last}}\,\,{	ext{diagram}}} ight)

https://preview.ibb.co/jsiRTe/04_Oct18_8t.gif

Let´s use UNITS CONTROL, one of the most powerful tools of our method!

{m{cyclist}}:\,\,\,5\min \,\,\left( {{{20\,\,{m{miles}}} \over {60\,\,\min }}\,\matrix{
 
earrow \cr 
 
earrow \cr

} } ight)\,\,\, = {5 \over 3}\,\,{m{miles}}

{m{hiker}}:\,\,\,{5 \over 3}{m{miles}}\,\,\left( {{{60\,\,{m{min}}} \over {4\,\,{m{miles}}}}\,\matrix{
 
earrow \cr 
 
earrow \cr

} } ight)\,\,\, = 25\,\,{m{minutes}}

Obs.: arrows indicate  licit converters .

? = 25 - 5\left( * ight) = 20\min

\left( * ight)\,\,{m{used}}\,\,{m{while}}\,\,\left( {{m{also}}} ight)\,\,{m{cyclist}}\,\,{m{was}}\,\,{m{moving}}!

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

Regards, 
Fabio.

AlN · Answer

Hi Sir,

I gt 25 minutes but I amnot able to understand why are we subtracting 5 from it.

fskilnik · Answer

Hi  AIN ,

Thank you for your interest in our solution!

During 5min the cyclist is able to run 5/3 miles (1st line), and the hiker needs 25min to run this distance (2nd line).

The fact is that the hiker "uses" 5min of "this" 25min while the cyclist runs 5/3 miles, therefore from the 25min needed by the hiker, he "saves" 5min using the interval of time before the cyclist stops!

Regards and success in your studies,
Fabio.

P.S.: more details related to the relative velocity (speed) are presented in our course.

sanjeevsinha082 · Answer

When cyclist stops, the distance between he and the hiker is 20*5-4*580
So, the cyclist will wait 80/420 minutes.

monkinaferrari · Answer

Relative Speed Ratio = 5x-x = 4x

Relative Time Taken by Cyclist = 5 mins
The time hiker will take = 5x4 = 20 mins

nikitathegreat · Answer

Why haven't we equted the total distance for cyclists in the above equation? 5/3 miles is the distance for only 5 mins and not the entire distance?

Regor60 · Answer

The question is looking only for the time from when the cyclist first passes the walker to when the walker catches up and because of this, information about what happens before they first meet doesn't matter.

Posted from my mobile device

DanTheGMATMan · Answer

Sort through the sequence of events and remember that the final catch-up episode means subtracting rates to get the rate of gain:

https://www.youtube.com/watch?v=yJPsYqc8J7Q

Aboyhasnoname · Answer

Relative Speed ... 16 Miles/ hr...... 
Cyclist travels for 16/60 in 1 minute and 16x5/60 in 5 mins..Means 4/3 miles... this is the distance between them when the cyclists stops.... Now... Hiker is walking at 4 miles per hour... he needs to cover 1/3rd of the distance... this means he will take 1/3rd of 1 hour which is 20 mins...Hence C...

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

Prep Toolkit

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