1. Grace and Allie are going to meet at the fountain near their houses. They both leave their houses at the same time. Allie passes Grace's house on her way to the fountain.
- Allie's walking rate is 2 meters per second.
- Grace's walking rate is 1.5 meters per second.
A. How many seconds will it take Allie to reach the fountain?
B. Suppose Grace's house is 90 meters from the fountain. Who will reach the fountain first, Allie or Grace? Explain why.
Answer (3)
Well, if the fountain is 90 meters from the fountain, to find Allie's distance, simply divide 2 by 90. 90/2 = 45
It will take Allie about 45 seconds to reach the fountain.
Obviously, Allie will reach the fountain first because she is walking more meters per second.
Allie will take 45 seconds to reach the fountain at her walking rate of 2 meters per second. Grace will take 60 seconds because her rate is 1.5 meters per second, so Allie will reach the fountain first.
To answer the student's questions, we first need to establish the relationship between rate (speed), distance, and time. The formula to find the time taken to cover a distance at a certain speed is time = distance / speed.
a. If Allie's walking rate is 2 meters per second, and we assume that the distance to the fountain is the same as from Grace's house, 90 meters, then it will take Allie 45 seconds to reach the fountain. This is calculated as: 90 meters / 2 meters per second = 45 seconds
b. Since Allie passes Grace's house on her way to the fountain, she has to travel the entire distance from her house to Grace's house and then to the fountain. If Grace is already starting at her house, which is 90 meters away from the fountain, she will reach the fountain in 60 seconds (since 90 meters / 1.5 meters per second = 60 seconds). Because Grace will reach the fountain in 60 seconds and Allie in 45 seconds, Allie will reach the fountain first.
Allie's walking time to the fountain is 45 seconds if her distance is the same as Grace's house (90 meters). Grace will take 60 seconds to reach the fountain. Therefore, Allie will arrive first due to her faster walking speed.
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