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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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12 Nov 2018, 09:24
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Difficulty:

95% (hard)

Question Stats:

42% (02:37) correct 58% (02:22) wrong based on 217 sessions

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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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05 Dec 2018, 03:02
4
UNSTOPPABLE12 wrote:

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.

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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12 Nov 2018, 09:45
5
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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12 Nov 2018, 11:01
1
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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04 Dec 2018, 09:29

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.
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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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21 Jan 2019, 18:23
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.

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Re: A boy walking along a road at 3 kilometers per hour is overtaken by a   [#permalink] 21 Jan 2019, 18:23
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