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

Question

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

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

(B)  20

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

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

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

nkin · Accepted Answer

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

chetan2u · Answer

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

dave13 · Answer

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

gmexamtaker1 · Answer

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.

ScottTargetTestPrep · Answer

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

Karastoyanov · Answer

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.

Hanzel101 · Answer

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

gurmukh · Answer

When truck covers 1 km boy covers 3/40
Distance between truck and boy at the time of breakdown = 
1-3/40=37/40
Required time =37/40×3
Time in minutes =37/2

Posted from my mobile device

AnishPassi · Answer

Video solution starts at 12:43 https://www.youtube.com/watch?v=Lwh4_FQTFXA YouTube link starting at the solution: https://www.youtube.com/watch?v=Lwh4_FQTFXA&t=763s

BrentGMATPrepNow · Answer

After passing the boy, the truck travels 1 kilometer at a speed of 40 kmh and then breaks down.   
Time for truck to travel 1 km = distance/speed = 1/40 hours

During those first 1/40 hours (pre-breakdown), the distance the boy walks = (rate)(time) = (3)(1/40) =  3/40  km
During those same 1/40 hours (pre-breakdown), the distance the truck traveled = 1 km    
The  additional  distance the boy must walk to reach the truck = 1 -  3/40  =  37/40  km

So, we want to determine the time (in minutes) it takes the boy (traveling at 3 kms per hour) to travel a distance of  37/40  km

First let's convert 3 kilometers per  hour  to 3/60 kilometers per  minute , which equals  1/20  kilometers per minute. 
 
 Time = distance/speed = ( 37/40 )/( 1/20 ) = (37/40)(20/1) = 37/2 = 18.5 minutes

Answer: E

Rail · Answer

The key here is, as someone noted, to understand that the truck needs 1.5 min to do 1km (3/2 minutes since it's travelling at 2/3 km per minute, aka 40km/h)

Given the fact above, you can easily see that, if in 1.5 min the truck does 1000m, in the same time the boy, moving at 1000m every 20 min (aka 3km per hour), would have done 1000/20*1.5=75m.

So the distance between the truck and the boy when the truck breaks down is actually 1000m-75m=925m

We know that the boy is travelling at 50m/min (aka 3km per hour), so 925m/50m/m=18.5 minutes.

This problem is difficult because you need first to take into account the time that the truck needs to do 1 km, then consider that, during that time, the boy also moved so the distance between the 2 actors is always less than 1 km.

mojizohan · Answer

Guys, the question says: how many minutes after the BREAKDOWN, not how many minutes after OVERTAKING, but it is solved as if it was saying the latter. it's got a problem, doesn't it?

Kinshook · Answer

Given: A boy walking along a road at 3 kilometers per hour is overtaken by a truck traveling at 40 kilometers per hour.
Asked: 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?

Time taken by truck to travel 1 km = 1/40 hr = 60/40 mins = 1.5 mins
Distance travelled by the boy in 1.5 mins = 3/60*1.5 = 1.5/20 = 3/40 km
Time taken by the boy to travel (1-3/40) km = 37/40*3 hr = 60*37/40*3 = 37/2 mins = 18.5 mins

Time taken by the boy after the breakdown to reach the truck = 18.5 mins

IMO E

kokus · Answer

Truck goes 40km per 60 minutes and it breaks down the 1km after passing the boy. Therefore, it has been traveling for 1.5 min or 90 seconds (40/60).
The boy covers 3km in 1h or 3000m in 1h. Hence, he walks 50m per minute. Therefore in the time between the truck passing him and the the truck breaking down he covered 75m (50*1.5=75).
There is 1km less the 75m for him to cover before he reaches the truck. He has to cover 925m by walking 50m a minute. 925/50 is 18.5 minutes.

Pujachoudhary · Answer

I really took 4 mins plus to solve this questions, got really confused in the conversions so that is one weak point to work on.
Let's break the problem down:
The boy takes 20 minutes to cover 1 km (3/60) min
The trucks takes 1.5 minutes to cover 1 km (60/40)min
By the time the truck reaches to the breakdown point, in 1.5 minutes
the boy has covered 75 metres in those 1.5 minutes (1.5*50=75m) (the boy covers 50 m in 1 minute) after being overtaken by the truck

Finally effective d = 1000-75=925m
Time taken by the boy to cover 925 m =925/50 = 18.5

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

Prep Toolkit

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