Cars P and Q started simultaneously from opposite ends of a straight 300-mile expressway and traveled toward each other, without stopping, until they passed atlocation X . To the nearest mile, how many miles of the expressway had car P traveled when the two cars passed each other?
(1) Up to location X , the average speed of car Q was 15 miles per hour faster than that of car P .
(2) Up to location X , the average speed of car Q was four by three times that of car P . ans?
Let's break down the information given:
Cars P and Q started simultaneously from opposite ends of a 300-mile expressway and traveled toward each other until they passed at location X.
We need to find out how many miles of the expressway car P traveled when the two cars passed each other.
Statement 1: Up to location X, the average speed of car Q was 15 miles per hour faster than that of car P.
This information alone is not sufficient to determine how many miles car P traveled. We don't have any specific information about the speeds of either car or the time it took for them to pass each other.
Statement 2: Up to location X, the average speed of car Q was four-thirds (4/3) times that of car P.
This information alone is not sufficient either. We still don't have any specific information about the speeds of either car or the time it took for them to pass each other.
Taking both statements together:
Using the information from both statements, we still don't have enough specific information about the speeds of either car or the time it took for them to pass each other.
Thus, the answer is (E) - The two statements together are still insufficient.
To find the number of miles car P traveled up to location X when the two cars passed each other, we need to determine the average speed of car P.
Let's break down the information given in the statement and the two statements provided:
Information given:
- Cars P and Q started simultaneously from opposite ends of a straight 300-mile expressway.
- They traveled toward each other without stopping until they passed at location X.
Statement 1: Up to location X, the average speed of car Q was 15 miles per hour faster than that of car P.
This statement implies that the average speed of car Q is known to be 15 miles per hour faster than that of car P. However, it doesn't provide the value of either car's average speed.
Statement 2: Up to location X, the average speed of car Q was four by three times that of car P.
This statement gives a ratio between the average speeds of car Q and car P. It states that car Q's average speed is four-thirds (4/3) times car P's average speed. However, it doesn't provide the specific values of their speeds.
To determine the distance car P traveled when the two cars passed each other, we need additional information about either car's average speed.
Therefore, the answer cannot be determined based on the given information and the statements.