GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 16:02

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 22 Jun 2014
Posts: 1093
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

### Show Tags

12 Nov 2018, 10:24
3
1
42
00:00

Difficulty:

95% (hard)

Question Stats:

46% (02:38) correct 54% (02:12) wrong based on 385 sessions

### HideShow timer Statistics

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

Project PS Butler : Question #13

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7959
Re: A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

### Show Tags

05 Dec 2018, 04:02
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
_________________
Manager
Joined: 09 Jun 2018
Posts: 188
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)
Re: A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

### Show Tags

12 Nov 2018, 10:45
11
1
1
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
_________________
If you found this relevant and useful, please Smash that Kudos button!
##### General Discussion
VP
Joined: 09 Mar 2016
Posts: 1230
A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

### Show Tags

12 Nov 2018, 12:01
2
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
Manager
Joined: 16 Jul 2018
Posts: 59
Re: A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

### Show Tags

04 Dec 2018, 10:29

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.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8069
Location: United States (CA)
Re: A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

### Show Tags

21 Jan 2019, 19:23
1
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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 03 May 2019
Posts: 14
Re: A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

### Show Tags

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.
Manager
Joined: 15 Jul 2016
Posts: 99
GMAT 1: 690 Q48 V36
Re: A boy walking along a road at 3 kilometers per hour is overtaken by a  [#permalink]

### Show Tags

18 Jul 2019, 05:41
1
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
_________________
Please give Kudos if you agree with my approach :)
Re: A boy walking along a road at 3 kilometers per hour is overtaken by a   [#permalink] 18 Jul 2019, 05:41
Display posts from previous: Sort by