Vincen wrote:Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other's point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?
(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) Train Q averaged a speed of 55 miles per hour for the entire trip.
OA is A.
I don't know how can I solve this DS question. Experts, can you give me some help.
Given: Total track distance is 250 miles. Trains P and Q left at same time. The two trains passed each other after 2 hours.
Target question: When the two trains passed, which train was nearer to its destination?
Statement 1: At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
KEY INFO: The two trains passed each other after traveling for
2 hours
During those two hours, train P averaged 70 mph
distance = (rate)(speed)
So, during those two hours, train P's travel distance = (70)(2) = 140 miles
Since the trains MEET after 2 hours, and since the total track distance is 250 miles, we can conclude that train Q traveled the 110 miles during the 2 hours.
The answer to the target question is
train P is closer to its destination
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: Train Q averaged a speed of 55 miles per hour for THE ENTIRE TRIP.
Note the ENTIRE TRIP part. Statement 2 doesn't really tell us much about the first 2 hours (until the trains met)
Let's examine two possible scenarios:
NOTE:
time = distance/rate
This means train Q's TOTAL travel time = 250/55 ≈ 4.5 hours
So, as long as train Q's TOTAL travel time is 4.5 hours, then statement 2 is satisfied
Case a: Train Q travels 150 miles in the first 2 hours and then travels 100 miles in the next 2.5 hours. Train P travels 100 miles in the first 2 hours and then travels 150 miles in the next 2 hours.
In this case, the answer to the target question is
train P is closer to its destination
Case b: Train Q travels 100 miles in the first 2 hours and then travels 150 miles in the next 2.5 hours. Train P travels 150 miles in the first 2 hours and then travels 100 miles in the next 2 hours.
In this case, the answer to the target question is
train Q is closer to its destination
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
