To determine how long Tammy will have to wait for Sue to arrive, we can analyze the given information about their travel times based on the graph descriptions you provided.
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Tammy's travel time: Tammy's travel time is represented by the point (6, 18). This means that Tammy arrives at the store after 6 units of time (let's say minutes) and at that point, she has spent a total of 18 minutes.
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Sue's travel time: The points provided for Sue show a straight line with the coordinates (1, 3), (2, 6), (3, 9), and so on. This suggests that Sue's travel time increases linearly. From the pattern, we can see that Sue's travel rate is 3 minutes for every 1 unit of time. Therefore, if \( t \) is the amount of time Sue travels, her total travel time can be described by the equation \( T_s = 3t \).
Now, we want to find out when Sue will arrive at the store.
- Since Tammy takes 6 minutes (time = 6) to reach the store, we can plug this value into Sue's equation: \[ T_s = 3 \times 6 = 18 \text{ minutes} \]
This means that both Tammy and Sue arrive at the store at the same time of 18 minutes.
Since Tammy arrives at the store at 6 minutes and Sue also arrives at 18 minutes, we can calculate how long Tammy waits for Sue:
- Wait time for Tammy: \[ \text{Wait time} = \text{Sue's Arrival Time} - \text{Tammy's Arrival Time} = 18 \text{ minutes} - 6 \text{ minutes} = 12 \text{ minutes} \]
Therefore, Tammy will have to wait for 12 minutes for Sue to arrive at the store.