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# Two cities, Kensington MD and Reston VA are 30 km a (m05q14)

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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  09 Dec 2010, 12:18
I think the OA is wrong since
"At the moment they do meet, the fly lands on the shoulder of the Kensington hiker as he continues his journey to Reston."
Suggests the flies speed reduces to 5 km/hr after the hiker meet.....
so it should be around 20+15+6.33(something)....
Please put some light on this...
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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  26 May 2011, 03:36
Time required to meet = 30/(5+5) = 3 hrs

Distance traveled by the Fly = 3 * 10 = 30

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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  26 May 2011, 05:33
I would propose a different way of solving this question.. Key point for me is

"When it reaches the Reston hiker, it turns around and flies back to the Kensington hiker"

Time to reach Reston from Kensington = 02 hours which is calculated by following method.

fly and Reston moving to each other ...> commutative speed = 15km/h
Total distance between them = 30km. .... > Time to meet ( Fly and Reston ) = 30/15 = 2hours

In 02 hours , Fly travels a distant = 2h * 10km/h = 20 Km ----------------- (a)

Mean while in two hours , Kensington has traveled = 5km/h * 2 = 10 km.

Distance between Fly and Kensington = 10 km.

Time in which Kensington and Fly meet = {10} km /{(10+5) km/h} = 2/3 hours

Second Distance traveled by Fly to Meet Kensington = 10Km/h * 2/3H = 20 /3 = 6.66 km ----- (b)

Fly Returns back after meeting Kensington , so there is a 3rd distance covered here

we know that the point where two hikers meet is = 15 km from each city.

So Remaining Distance = 15 - 10 - 3.333 = 1.666

3rd distance covered by fly = 10 * 1.666 /5 = 3.333 km ------------- (c)

Adding a , b & C ... > Total distance covered by Fly = 30 km .
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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  26 May 2011, 12:08
The words got to me.
The solution is quite simple
Fly has flown for 3hrs at the speed of 10km/hr
So ans is B: 30km
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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  29 May 2011, 03:15
Should have answered b) 30 but I added 15. Rushed the question.
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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  03 May 2012, 12:08
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arjtryarjtry wrote:
Two cities, Kensington MD and Reston VA are 30 km apart. From both of these cities, simultaneously, two hikers start their journeys towards each other. They are walking at a constant speed of 5 km/hour each. Simultaneously, a fly leaves the city of Kensington. It flies at the speed of 10 km/hour and passes the hiker from its city. When it reaches the Reston hiker, it turns around and flies back to the Kensington hiker. It keeps doing so until the hikers meet. At the moment they do meet, the fly lands on the shoulder of the Kensington hiker as he continues his journey to Reston. How many kilometers has the fly flown?

(A) 25
(B) 30
(C) 37.5
(D) 45
(E) 60

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

First of all I'd remove the "the fly lands on the shoulder of the Kensington hiker as he continues his journey to Reston" part.

The question basically asks: how many kilometers is covered by fly by the time two hikers meet.

Notice that the fly travels all the time till the hikers meet, so for 30/(5+5)=3 hours, which means that the fly covers Rate*Time=Distance --> 10*3=30 kilometers.

Hope it's clear.
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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  03 May 2012, 20:27
It is clear. Thanks Bunuel!
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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  30 May 2012, 05:45
The relative speed (velocity) of the two hikers is 5 + 5 = 10 km/hr. The two hirers put together covered a distance of 30 kms.
T = D / R => T = 30 / 10 = 3 Hours

In the meantime, the flier continues to fly at the rate of 10 km/hr. So, in three hours the flier will travel:
D = RT = 10 * 3 = 30 km.

B is the correct answer. Excellent Problem!!

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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  30 May 2012, 10:04
Expert's post
Bunuel wrote:
arjtryarjtry wrote:
Two cities, Kensington MD and Reston VA are 30 km apart. From both of these cities, simultaneously, two hikers start their journeys towards each other. They are walking at a constant speed of 5 km/hour each. Simultaneously, a fly leaves the city of Kensington. It flies at the speed of 10 km/hour and passes the hiker from its city. When it reaches the Reston hiker, it turns around and flies back to the Kensington hiker. It keeps doing so until the hikers meet. At the moment they do meet, the fly lands on the shoulder of the Kensington hiker as he continues his journey to Reston. How many kilometers has the fly flown?

(A) 25
(B) 30
(C) 37.5
(D) 45
(E) 60

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

First of all I'd remove the "the fly lands on the shoulder of the Kensington hiker as he continues his journey to Reston" part.

The question basically asks: how many kilometers is covered by fly by the time two hikers meet.

Notice that the fly travels all the time till the hikers meet, so for 30/(5+5)=3 hours, which means that the fly covers Rate*Time=Distance --> 10*3=30 kilometers.

Hope it's clear.

Bunuel we can reason in a similar way: rate constant for each and also distance. R= 6 ---> Fly D = r*t ---> 10*6 = 60.

Considering that the fly meets runner in the middle (where they meet each other) we have 30. It is correct or prone of error ??'

thanks
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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  31 May 2012, 02:13
Expert's post
carcass wrote:
Bunuel wrote:
arjtryarjtry wrote:
Two cities, Kensington MD and Reston VA are 30 km apart. From both of these cities, simultaneously, two hikers start their journeys towards each other. They are walking at a constant speed of 5 km/hour each. Simultaneously, a fly leaves the city of Kensington. It flies at the speed of 10 km/hour and passes the hiker from its city. When it reaches the Reston hiker, it turns around and flies back to the Kensington hiker. It keeps doing so until the hikers meet. At the moment they do meet, the fly lands on the shoulder of the Kensington hiker as he continues his journey to Reston. How many kilometers has the fly flown?

(A) 25
(B) 30
(C) 37.5
(D) 45
(E) 60

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

First of all I'd remove the "the fly lands on the shoulder of the Kensington hiker as he continues his journey to Reston" part.

The question basically asks: how many kilometers is covered by fly by the time two hikers meet.

Notice that the fly travels all the time till the hikers meet, so for 30/(5+5)=3 hours, which means that the fly covers Rate*Time=Distance --> 10*3=30 kilometers.

Hope it's clear.

Bunuel we can reason in a similar way: rate constant for each and also distance. R= 6 ---> Fly D = r*t ---> 10*6 = 60.

Considering that the fly meets runner in the middle (where they meet each other) we have 30. It is correct or prone of error ??'

thanks

Sorry, but I don't understand your approach at all.
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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  31 May 2012, 05:52
Expert's post
Sorry

Ok I try to explain.

R*T = D

K - 5 * t = 30

V - 5 * t = 30

K Time = 6
V Time = 6

Fly 10*6 = 60 (distance) but from this wording problem (a lot convoluted) the fly flight for half of distance (is the only logic thing to think, also because the hikers in their time and distance are constant).
Thanks Gmatclub!!
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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  30 May 2013, 20:17
arjtryarjtry wrote:
Two cities, Kensington MD and Reston VA are 30 km apart. From both of these cities, simultaneously, two hikers start their journeys towards each other. They are walking at a constant speed of 5 km/hour each. Simultaneously, a fly leaves the city of Kensington. It flies at the speed of 10 km/hour and passes the hiker from its city. When it reaches the Reston hiker, it turns around and flies back to the Kensington hiker. It keeps doing so until the hikers meet. At the moment they do meet, the fly lands on the shoulder of the Kensington hiker as he continues his journey to Reston. How many kilometers has the fly flown?

(A) 25
(B) 30
(C) 37.5
(D) 45
(E) 60

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

B
Since the fly flies for 3 hours at 10km/hr

And, awkward wording aside, seems like a great question. I started out calculating it segmentally, then realized what the question boils down to, which cost me a good minute of useless calculations.
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Re: problemmmmmm..... too good!!! (m05q14) [#permalink]  01 Jun 2013, 05:12
this OA is right

30/3=10

10/3 = 3.33

3.333/3 = 1.111

1.111/3 = 033388

0.388/3 = 0.1xyz..bla bla

=15

15*2 =30 well right

why *2 -> its fly not hiker- please take pen and paper and draw a pic and then sort it

why /3 because fly speed it /3 part of distance
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Re: Two cities, Kensington MD and Reston VA are 30 km a (m05q14) [#permalink]  22 May 2014, 07:14
trick is to calculate the amount of time it takes for the two hikers to meet:
Each travel at 5 km/hr --> Each travel 15 km
15 km / 5 km/hr = 3 hrs

The fly travels for 3 hrs at 10mph
Total distance = 3hrs * 10mph = 30 miles
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Re: Two cities, Kensington MD and Reston VA are 30 km a (m05q14) [#permalink]  23 May 2014, 08:44
Simple method:

They are approaching each other at a speed of 5+5 = 10km/hr.
They need to cover 30 km, so time needed = $$\frac{30}{10} = 3$$ hrs

So, Total distance covered by the fly in 3hrs = 10mph* 3hrs = 30 miles

Rgds,
Rajat
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Re: Two cities, Kensington MD and Reston VA are 30 km a (m05q14)   [#permalink] 23 May 2014, 08:44

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# Two cities, Kensington MD and Reston VA are 30 km a (m05q14)

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