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

 It is currently 16 Jul 2018, 17:24

### 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

# Alice and Bob traveled in the same direction along the same route at t

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5836
GMAT 1: 760 Q51 V42
GPA: 3.82
Alice and Bob traveled in the same direction along the same route at t [#permalink]

### Show Tags

21 Mar 2018, 02:52
00:00

Difficulty:

35% (medium)

Question Stats:

74% (02:34) correct 26% (01:57) wrong based on 62 sessions

### HideShow timer Statistics

[GMAT math practice question]

Alice and Bob traveled in the same direction along the same route at their respective constant speeds of 12 km per hour and 6 km per hour. They each started to travel from their own houses. Bob’s house is halfway between Alice’s house and the destination. After passing Bob, Alice took 10 minutes to reach the destination. How many minutes did it take Bob to reach the destination after Alice passed him?

A. 5 min
B. 6 min
C. 8 min
D. 10 min
E. 20 min

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" BSchool Forum Moderator Joined: 07 Jan 2016 Posts: 727 Location: India GMAT 1: 710 Q49 V36 Alice and Bob traveled in the same direction along the same route at t [#permalink] ### Show Tags 21 Mar 2018, 03:12 1 MathRevolution wrote: [GMAT math practice question] Alice and Bob traveled in the same direction along the same route at their respective constant speeds of 12 km per hour and 6 km per hour. They each started to travel from their own houses. Bob’s house is halfway between Alice’s house and the destination. After passing Bob, Alice took 10 minutes to reach the destination. How many minutes did it take Bob to reach the destination after Alice passed him? A. 5 min B. 6 min C. 8 min D. 10 min E. 20 min Since the speed of Alice is double the speed of bob, the time taken by alice is half the time taken by Bob Alice takes 10 mins thus bob takes $$\frac{10}{1/2}$$ = 10 x2 = 20 (E) SC Moderator Joined: 22 May 2016 Posts: 1825 Alice and Bob traveled in the same direction along the same route at t [#permalink] ### Show Tags 21 Mar 2018, 10:38 MathRevolution wrote: [GMAT math practice question] Alice and Bob traveled in the same direction along the same route at their respective constant speeds of 12 km per hour and 6 km per hour. They each started to travel from their own houses. Bob’s house is halfway between Alice’s house and the destination. After passing Bob, Alice took 10 minutes to reach the destination. How many minutes did it take Bob to reach the destination after Alice passed him? A. 5 min B. 6 min C. 8 min D. 10 min E. 20 min Convert rates to minutes. A's rate in minutes: $$\frac{12km}{1hr}=\frac{12km}{60mins}=\frac{1km}{5mins}$$ B's rate in minutes: $$\frac{6km}{1hr}=\frac{6km}{60mins}=\frac{1km}{10mins}$$ Information to ignore or avoid: 1) Bob's house as a halfway point 2) Relative speed 3) Whatever happens before the passing point As soon as Alice passes Bob, the chase is over. Both travel the same distance to the end.* We need only two pieces of information: 1) the distance from pass point to end, which we can derive from Alice's time; and 2) the time it takes for Bob to travel that distance, which we can derive from his rate Distance to end In 10 minutes, the distance Alice covers is $$D= R*T$$, so $$D= \frac{1km}{5mins}* 10mins = 2$$ kilometers Time Bob takes to cover distance of 2km $$R*T= D$$, so $$T =\frac{D}{R}$$ $$T =\frac{2km}{\frac{1km}{10mins}}=(2km*\frac{10mins}{1km})= 20$$ minutes Answer E * Distance from pass point to end is same for both Point at which A passes B House B--->---B|------------| House B---->--A|------------| A is in front of B House B--->--->|B->---------| House B---->-->|-----A-->---| _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5836 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Alice and Bob traveled in the same direction along the same route at t [#permalink] ### Show Tags 23 Mar 2018, 00:22 => After Alice passed Bob, she traveled for $$10$$ more minutes. Since Bob’s speed is half of Alice’s speed, he took a further $$20$$ minutes to reach the destination. Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 23 Oct 2013
Posts: 3
Re: Alice and Bob traveled in the same direction along the same route at t [#permalink]

### Show Tags

24 Mar 2018, 19:42
If bob house is halway between alice and destination and if slice speed is twice that of bob

How are they supposed to cross each other they will meet directly at destination

alice has to cover 2d distance with 12km/hr implies time taken is 2d/12=d/6

bob jas to travel d with speed 6km/hr hence time taken is d/6

so they meeet directly in destination

SC Moderator
Joined: 22 May 2016
Posts: 1825
Alice and Bob traveled in the same direction along the same route at t [#permalink]

### Show Tags

24 Mar 2018, 22:06
sameeruce08 wrote:
If bob house is halway between alice and destination and if slice speed is twice that of bob

How are they supposed to cross each other they will meet directly at destination

alice has to cover 2d distance with 12km/hr implies time taken is 2d/12=d/6

bob jas to travel d with speed 6km/hr hence time taken is d/6

so they meeet directly in destination

sameeruce08 , the "halfway" info is to let us know that Alice starts behind Bob.

As far as distance:
A does travel 2d, but we don't care about that because we don't know start times.

After she passes him, both travel same distance.

We find distance from her rate and time. In minutes. (Or fraction of hour.)

Then find Bob's time from distance and rate.

All that matters: separate rates and times.

She travels at 12 km per hour.
One hour = 60 minutes.
Rate: She travels 12 km in 60 minutes:
D= $$(\frac{12km}{60mins}*10 minutes) = 2$$ kms

Bob's speed = 6 km/hr, OR 6 km in 60 minutes.

Bob's time?
$$T = \frac{D}{R}$$
$$T = \frac{2}{(\frac{6}{60})} = (2 * \frac{60}{6})=20$$
minutes

OR get time from Bob's unit rate = $$\frac{6km}{60mins} =\frac{1km}{10mins}$$

To go 2 km, at a rate of 1 km per 10 minutes, it will take him 2 * 10 = 20 minutes.

Hope that helps.
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Alice and Bob traveled in the same direction along the same route at t   [#permalink] 24 Mar 2018, 22:06
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.