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A boy walking along a road at 3 kilometers per hour is overtaken by a

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A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

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New post 12 Nov 2018, 10:24
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A boy walking along a road at 3 kilometers per hour is overtaken by a truck traveling at 40 kilometers per hour. If the truck breaks down 1 kilometer beyond where it passes the boy, how many minutes after the breakdown does the boy reach the truck?


(A) \(21 \frac{1}{2}\)

(B) \(20\)

(C) \(18 \frac{34}{37}\)

(D) \(18 \frac{26}{43}\)

(E) \(18 \frac{1}{2}\)


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Re: A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

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New post 05 Dec 2018, 04:02
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UNSTOPPABLE12 wrote:
chetan2u VeritasKarishma Bunuel

Hello,
Could someone please explain the flaw of my approach?
My thinking process was that the truck will cover +1km thus the boy has to walk for u=x/t => 1/3h = 20m to reach the truck.
Thank you in advance.


Yes but the boy has also traveled for the time the truck took to travel 1 km..
So truck traveled 1 km in 60/40 or 1 and 1/2 minutes..
Thus the boy has traveled this 1.5 minutes distance by the time truck breaks down and the time is calculated thereafter, so 20-1.5=18.5
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Re: A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

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New post 12 Nov 2018, 10:45
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Truck travels 40 km in 60 min. So, it travels 1 km in 60/40 = 3/2 - 1.5 minutes.

Boy travels 3 km in 60 min, so he travels 1 km in 20 min.

Breakdown happens after 1.5 minutes of travel. The boy hence takes 20-1.5 minutes to reach the breakdown spot = 18.5 min

IMO, Option E
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A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

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New post 12 Nov 2018, 12:01
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Time taken for a truck to cover \(1km\) is \(\frac{1km}{40}*60 min\) = \(\frac{3}{2}\) i.e \(1.5\) during this period boy covered \(\frac{3}{40}\) of distance and time taken to cover the distance after breakdown is \(\frac{1-\frac{3}{40}}{3}*60 = 18.5\)


E :)
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Re: A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

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New post 04 Dec 2018, 10:29
chetan2u VeritasKarishma Bunuel

Hello,
Could someone please explain the flaw of my approach?
My thinking process was that the truck will cover +1km thus the boy has to walk for u=x/t => 1/3h = 20m to reach the truck.
Thank you in advance.
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Re: A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

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New post 21 Jan 2019, 19:23
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HKD1710 wrote:
A boy walking along a road at 3 kilometers per hour is overtaken by a truck traveling at 40 kilometers per hour. If the truck breaks down 1 kilometer beyond where it passes the boy, how many minutes after the breakdown does the boy reach the truck?


(A) \(21 \frac{1}{2}\)

(B) \(20\)

(C) \(18 \frac{34}{37}\)

(D) \(18 \frac{26}{43}\)

(E) \(18 \frac{1}{2}\)


Since it takes the truck 1/40 hour to travel 1 kilometer, the boy travel 3 x 1/40 = 3/40 kilometer during the same time. Thus he needs to travel 1 - 3/40 = 37/40 kilometer to catch up with the truck and that will take him (37/40)/3 = 37/120 hour or 37/120 x 60 = 37/2 =18.5 minutes.

Alternate Solution:

This is a 2-part problem. The first part is the time during which the truck passes the boy until the truck breaks down. The boy is walking during this time. Since the truck is traveling at 40 km/hour, then he takes 1/40 hour to travel the one km until his breakdown. The boy, during this 1/40 hour, has traveled 3 x 1/40 = 3/40 kilometers.
Now for part two of the problem. At the moment that the truck breaks down, the boy is now 1 - 3/40 = 37/40 kilometers behind the truck. Since he is walking at 3 km/hour, it will take him (37/40)/3 = 37/120 hours to catch up to the truck. We convert this to minutes: 37/120 x 60 = 37/2 = 18.5 minutes.

Answer: E
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Re: A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

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New post 21 May 2019, 13:58
1. Speed of the truck is 40km/h i.e. 40km/60 min.
2. The truck bypassed the boy and stopped 1km from the point of bypassing the boy. It took the truck 1.5min to travel 1km (60min/40km=1.5min).
3. During this time the boy was walking - meaning that during 1.5min he was walking.
4. The speed of the boy is 3km/h, meaning 1km per 20 min.
5. It takes him 20 min per 1 km, but he already was going from 1.5min, so the time left to go to reach the truck is 20-1.5=18.5min

Writing this not because I'm smart :) but to remember the solution better. That's what I recommend - explain it to yourself in your own words and share it - may be it will be of help to somebody.
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Re: A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

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New post 18 Jul 2019, 05:41
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This question can also be solved by Relative Speed method where the formula for relative speed is = d/(v2-v1)

1) We need to keep in mind that while the truck is moving for 1km, the boy is also walking. So, even though the truck moved for 1 km, the distance between the boy and the truck will be less than 1 km.
2) We apply the relative speed formula :

time = distance/difference in speeds

1/40 (i.e. the time taken by truck to complete 1 km) = d/(40-3)

==> d = 37/40.

Now, this is the net distance that has to be covered by the boy.

So, time taken by the boy to cover 37/40 km is

==> 37/40 * 60/3 = 37/2

Ans. E

Similar Q to practice https://gmatclub.com/forum/a-hiker-walk ... 04534.html
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Re: A boy walking along a road at 3 kilometers per hour is overtaken by a   [#permalink] 18 Jul 2019, 05:41
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