Final answer:
By calculating 2/3 of the distances in streets and avenues between Ping's and Ari's homes, we find that the gym should theoretically be located at the corner of 15th street and 14th avenue. However, this location does not match any of the options given, suggesting a possible mistake in the question or the answer choices.
Step-by-step explanation:
The student is asking about a mathematical calculation involving distance on a grid of streets and avenues. To find the location of the gym, we can use the concept of ratios and proportions. First, we need to determine the distance between Ping's home at the corner of 3rd street and 6th avenue, and Ari's home at the corner of 21st street and 18th avenue. We'll look at the street numbers and avenue numbers separately.
To find the distance along the streets, subtract Ping's street from Ari's: 21 - 3 = 18 streets. For the avenues: 18 - 6 = 12 avenues. Now, we want the gym to be 2/3 the distance from Ping's home to Ari's home. So, we'll take 2/3 of each of these distances. For the streets: (2/3) × 18 = 12. For the avenues: (2/3) × 12 = 8.
Starting from Ping's home, if we move 12 streets and 8 avenues, we get to the gym's location. Add 12 streets to 3rd street to get 15th street. Add 8 avenues to 6th avenue to get 14th avenue. Therefore, the gym is located at the corner of 15th street and 14th avenue, which corresponds to none of the choices given, indicating that there may be an error in the question or in the choices provided.