Driving at their respective constant speeds along the same route,

­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 could you help answer this one please?

Is this a catch up type 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?

"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

For Statement 1, I wrote the equation as:

(r+24)t = r(t+1) (since V was driving an hour more ahead of A)
I think what I did wrong was substitute 4 into t, so I got r = 96.

Could you help me understand why t should be 3 for Alfred? Should I rewrite the eqaution as:
(r+24)(t-1) = rt? MartyMurray

­i'm not sure what r or t represents here, but 96 might be resulted from "names' gender issue" that is not a issue for native speakers but could be a big one for non-native speakers.

Alfred is a male name, and Violet is female.

\(4V = 3(V + 24)\)
\(V = 72\)

if you misunderstood that pronoun—she—belongs to Alfred, you would get \(5V = 4(V + 24)\) and \(V = 96\).
 ­

­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.

­