Al and Harpreet are racing to Wing Stop to get the last batch of fries made for lunch. Al participates in cross country and can cover (write in value) per minute. Harpreet likes to watch TV and play video games. She is out of shape and can only cover 3 units per minute. If both students start at the same time from their given positions (write in value), who will make it to wing stop first? at what point on the coordinate grid will Al over take Harpreet.
On coordinate plane: (-5,3), Al:(-2,3), Building B (5,3), Harpreet (5,1), road (5,-3), and wing stop (-5,3)
To determine who will make it to Wing Stop first, we need to calculate the time it takes for both Al and Harpreet to reach their destination.
First, let's calculate the distance between Al's starting point and Wing Stop. Using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((-5 - (-2))^2 + (3 - 3)^2)
d = √((-5 + 2)^2 + (0)^2)
d = √((-3)^2 + (0)^2)
d = √(9 + 0)
d = √9
d = 3 units
Since Al's speed is (write in value) per minute, it will take him 3 units/(write in value) = (time) to reach Wing Stop.
Now let's calculate the distance between Harpreet's starting point and Wing Stop:
d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((-5 - 5)^2 + (3 - 1)^2)
d = √((-10)^2 + (2)^2)
d = √(100 + 4)
d = √104
d ≈ 10.2 units
Since Harpreet's speed is 3 units per minute, it will take her 10.2 units/3 units per minute ≈ 3.4 minutes to reach Wing Stop.
Therefore, Al will make it to Wing Stop first, as he will take less time compared to Harpreet.
To find the point at which Al overtakes Harpreet on the coordinate grid, we need to consider their positions and speeds.
Al's position is (-2, 3), and Harpreet's position is (5, 1).
The difference in x-coordinates is 5 - (-2) = 7.
Since Al's speed is greater than Harpreet's, he will catch up to her at a rate of (write in value) units per minute.
Using the formula: time = distance / speed, we can calculate the time it takes for Al to catch up to Harpreet:
time = 7 units / (Al's speed - Harpreet's speed)
time = 7 units / ((write in value) - 3 units per minute)
Once you have calculated the time, you can determine the point of intersection by finding Al's position at that time using the formula: distance = speed × time.
The final coordinate at which Al overtakes Harpreet would be (x, y), where x is Al's initial x-coordinate minus the distance covered, and y is Al's initial y-coordinate.