Rationale
Maria will walk 7x/15 yards in the next 7 minutes.
To determine how many more yards Maria will walk in 7 minutes, we first calculate her walking rate, which is x yards in 15 minutes. By finding her average speed, we can then project the distance she covers in the additional time.
A) 15x/7
This choice incorrectly represents the distance covered in 7 minutes. The expression suggests a calculation based on a fixed fraction of the total distance walked in a different context rather than the average rate. It does not take into account the correct time interval or the relationship between distance, rate, and time.
B) (x/15)+7
This option inaccurately adds a constant to the average rate, implying that Maria walks an extra 7 yards on top of her actual speed. The formula does not correctly reflect the relationship among distance, time, and rate, leading to a nonsensical result that does not represent her walking distance in the specified time frame.
C) (x+7)/15
This choice implies an incorrect average speed calculation by summing the total distance with 7 yards and then dividing by 15. This approach fails to represent the time correctly and distorts the relationship between distance and rate, leading to an erroneous average speed rather than the actual distance covered in the next 7 minutes.
D) 7x/15
This choice accurately calculates the distance Maria will walk in 7 minutes. By first determining her speed as x/15 yards per minute, we multiply this rate by 7 minutes, leading to the correct formula of (x/15) * 7 = 7x/15 yards.
Conclusion
Maria's walking distance in 7 minutes can be accurately calculated using her established average rate of x yards in 15 minutes. The correct choice, 7x/15, derives from multiplying her speed by the time interval, ensuring the calculation aligns with the principles of distance, rate, and time. The other options misinterpret these relationships, leading to incorrect conclusions.
