Driving at their respective constant speeds along the same route,

Question

Driving at their respective constant speeds along the same route, Alfred passed a certain landmark 1 hour after Violet did. Both Alfred and Violet continued driving along the same route in the same direction at their respective constant speeds. If Alfred's speed was 24 kilometers per hour greater than Violet's, what was Violet's speed?

(1) Alfred overtook Violet 4 hours after she passed the landmark.
(2) Alfred's speed was 4/3 of Violet's speed.

Show Spoiler

Attachment:

Distance.png [ 67.67 KiB | Viewed 11868 times ]

Show Answer

Official Answer

D

Bunuel · Accepted Answer

Driving at their respective constant speeds along the same route, Alfred passed a certain landmark 1 hour after Violet did. Both Alfred and Violet continued driving along the same route in the same direction at their respective constant speeds. If Alfred's speed was 24 kilometers per hour greater than Violet's, what was Violet's speed?

(1) Alfred overtook Violet 4 hours after she passed the landmark.
(2) Alfred's speed was 4/3 of Violet's speed.

Show Spoiler

Attachment:

Distance.png

Let's assign Violet's speed as x kilometers per hour. Therefore, Alfred's speed is x + 24 kilometers per hour.

The distance between Alfred and Violet, at the time Alfred passed the landmark, equates to the distance Violet covered in 1 hour, which is x kilometers (since Violet passed the landmark 1 hour before Alfred).

(The landmark/Alfred) ---------- (1 hour * x km/h= x kilometers) ---------- (Violet)  
 
(1) Alfred overtook Violet 4 hours after she passed the landmark.

Considering Alfred passed the landmark 1 hour after Violet, it indicates that Alfred closed a gap of x kilometers in 3 hours after he passed the landmark. With their relative speed being 24 kilometers per hour (x + 24 - x), we deduce x/24 = 3, leading us to x = 72 kilometers per hour.

Sufficient.

(2) Alfred's speed was 4/3 of Violet's speed.

This implies that x + 24 = 4/3*x, which also gives x = 72 kilometers per hour.

Sufficient.

Answer: D.

sanebeyondone · Answer

With all due respects, I'm not sure what this means
With their relative speed being 24 kilometers per hour (x + 24 - x), we deduce x/24 = 3

though I understand that with the rule of three in arithmetic (comparing ratio)
X   / 24   = 3 hr / 1 hr
then X = 72
I understand relative speed but I'm not sure what is "deduce" that Bunuel said.

using the conventional V=S/T formula results strangely. Could anyone show how to use V=S/T formula to solve this question?

Bunuel · Answer

Their relative speed was 24 kilometers per hour, and the distance between them was x kilometers. Alfred closed this gap in 3 hours, thus (time) = (distance)/(ralaitive spees) = x/24 = 3 hours.

MartyMurray · Answer

Driving at their respective constant speeds along the same route, Alfred passed a certain landmark 1 hour after Violet did. Both Alfred and Violet continued driving along the same route in the same direction at their respective constant speeds. If Alfred's speed was 24 kilometers per hour greater than Violet's, what was Violet's speed?

(1) Alfred overtook Violet 4 hours after she passed the landmark.
(2) Alfred's speed was 4/3 of Violet's speed.

Show Spoiler

Attachment:

Distance.png

"Alfred passed a certain landmark 1 hour after Violet did," can be taken to mean, basically, that Alfred started an hour after Violet did.

So, if Violet's speed is v kilometers per hour, Violet had gone v kilometers when Alfred started.

Then, Alfred's speed is v + 24. So, as they both drive, Alfred is catching up with Violet.

(1) Alfred overtook Violet 4 hours after she passed the landmark.

We can intuitively tell that we can find Violet's speed using this information. After all, from the question stem, we already know the absolute difference between their speeds, 24 kilometers per hour, and from this statement, we now know for how many hours Alfred had to driver 24 kilometers per hour faster than Violet to catch up to her. So, it makes sense that we'd be able to calculate their speeds given what the passage and this statement say.

In fact, using the information from the passage and this statement, we can calculate Violet's speed in mutiple ways.

One way is to use this statement and what the passage says about Alfred passing the landmark an hour after Violet did to determine the following.

4 hours after Violet passed the landmark, when Alfred caught up, Violet had driven for 4 hours, and Alfred had driven for three hours. So, Violet and Alfred went the same distance in 4 and 3 hours respectively.

Thus, Alfred's speed is 4/3 Violet's speed.

So, v + 24 = 4v/3.

Without doing any more math, we can see that we can use that equation to find the value of v.

Another way to determine Violet's speed is to see that Alfred had to go 24 kilometers per hour faster than Violet for 3 hours to catch up to her while she was driving.

So, he had to make up 3 x 24 = 72 kilometers of distance to catch up to Violet. That information means that, in the first hour before Alfred passed the landmark, Violet went 72 kilometers. So, her speed is 72 kilometers per hour.

Sufficient.

(2) Alfred's speed was 4/3 of Violet's speed.

We know that Alfred's speed is v + 24.

Now, using this statement, we also know the following:

v + 24  = 4v/3

Without doing any more math, we can see that we can use that equation to find the value of v.

So, statement (2) is sufficient, and probably, the question-writer considered this question somewhat of a B trap question, because it's relatively easy to see that statement 2 is sufficient while it's not as easy to tell that statement 1 is sufficient.

Sufficient.

Correct answer:  D

GMATGuruNY · Answer

Let A = Alfred's speed and V = Violet's speed.
Question stem: What is the value of V?
Since Alfred's speed is 24 kph faster than Violet's, A-V = 24.

Statement 1:
Let's say Violet passes the landmark at noon.
Since she is overtaken by Alfred 4 hours later -- at 4pm -- her travel time is 4 hours.
Alfred passes the landmark 1 hour after Violet does -- at 1pm -- and overtakes her at 4pm, implying that Alfred's travel time is 3 hours.
Time and rate have a RECRIPROCAL RELATIONSHIP.
Since the time ratio for Alfred and Violet is 3/4, their rate ratio is 4/3:
A/V = 4/3
Since we have two variables (A and V) and two distinct linear equations (A-V = 24 and A/V = 4/3), we can solve for the two variables.
SUFFICIENT.

Statement 2:
A = (4/3)V
Since we have two variables (A and V) and two distinct linear equations (the equatiion above and A-V = 24), we can solve for the two variables.
SUFFICIENT.

D

ManishaPrepMinds · Answer

Statement 1 Analysis: 
Let Violet’s speed be v km/hr.
Alfred passed the landmark 1 hour later than Violet.
Alfred overtakes Violet 4 hours after she passed, so Alfred drove for 3 hours before catching up.
During her 1-hour head start, Violet covered:
Distance = v × 1 = v km

Alfred’s relative speed = 24 km/hr (since he's 24 km/hr faster).
Time to catch up = 3 hours
Distance Alfred gained = 24 × 3 = 72 km

So, Violet’s 1-hour lead distance (v) = 72 km
 v = 72 km/hr
Statement (1) is sufficient.

Statement 2 Analysis  
Alfred’s speed was 4/3 of Violet’s speed.
Let Violet’s speed = v km/hr
Then Alfred’s speed = (4/3)v
It is also given that Alfred’s speed is 24 km/hr more than Violet’s.
So:
(4/3)v – v = 24
(1/3)v = 24
v = 72
So, Violet’s speed is  72 km/hr .
 Statement (2) alone is sufficient.

Answer: D

KeshavKapoor · Answer

Each statement ALONE is sufficient to answer the question - Option D

Let V be Violet's speed and A be Alfred's speed, both in kilometers per hour (km/h). From the problem description, we know two key pieces of information:
 
 Alfred's speed is 24 km/h greater than Violet's: A=V+24. 
 Alfred passes a landmark 1 hour after Violet. We need to find V.  
To solve for the two unknown speeds (A and V), we need another independent equation relating them.

Statement (1)

(1) Alfred overtook Violet 4 hours after she passed the landmark. 
This statement means that 4 hours after Violet passed the landmark, Alfred and Violet were at the same position. Let's calculate their distances from the landmark at that moment.
 
  Violet's distance:  In 4 hours, Violet travels a distance of dV=V×4. 
  Alfred's distance:  Since Alfred passed the landmark 1 hour after Violet, he has only been driving for 4−1=3 hours. His distance is dA=A×3.  
When Alfred overtakes Violet, their distances are equal: dA=dV => 3A=4V
Now we have a system of two equations:
 
 A=V+24 
 3A=4V  
Substituting the first equation into the second gives: 3(V+24)=4V => 3V+72=4V => V=72 km/h
Since we can find a unique value for Violet's speed,  Statement (1) is sufficient.

Statement (2)

(2) Alfred's speed was 4/3 of Violet's speed. 
This statement gives us a direct mathematical relationship between their speeds: SA=34SV
Now we can use this equation with the one from the initial problem description:
 
 A=V+24 
 A=4/3V  
Setting the two expressions for A equal to each other: V+24=4/3V => 24=4/3V−V => 24=1/3V => V=72 km/h
Since we can find a unique value for Violet's speed,  Statement (2) is also sufficient.

DonBosco7 · Answer

Hi Bunuel , Please check the steps below and help me understand what is wrong with this approach. https://gmatclub.com/forum/download/file.php?id=85815 GMAT-Club-Forum-5vjomczn.png

Bunuel · Answer

Please study solution posted  HERE :

Violet passes the landmark at time 0. 
 Alfred passes the same landmark 1 hour later.  At that moment, Violet is already x km ahead.  
 Alfred catches up  4 hours after Violet passed the landmark . 
 So Alfred only had  3 hours  after  he  passed the landmark to close the x-km gap.

Relative speed = 24 km/h. So time to overtake after Alfred passes the landmark = x/24 = 3, which give x = 72.

Driving at their respective constant speeds along the same route,

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Driving at their respective constant speeds along the same route,

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards