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

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

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.

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

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.

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

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

Video solution starts at 12:43



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

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 [given information]
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

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.

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?

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