Alright, let's analyze the situation step-by-step to determine which statements are true.
1. Understanding Brendon's situation:
- Brendon is walking from a place that is 1.5 miles away. We know that 1 mile is 5280 feet.
- Converting 1.5 miles to feet, we get 1.5 * 5280 = 7920 feet.
- The function given is [tex]\( y = 7920 - 270x \)[/tex], where [tex]\( y \)[/tex] represents Brendon's distance from home in feet, and [tex]\( x \)[/tex] is the number of minutes he walks.
- Brendon’s initial distance from home is 7920 feet.
- Brendon's speed is 270 feet per minute.
2. Understanding Bryan's situation:
- From the table:
- At 0 minutes, the distance is 8000 feet.
- At 15 minutes, the distance is 3800 feet.
- To find Bryan's speed, we calculate the distance he covers in 15 minutes:
- Initial distance = 8000 feet
- Distance after 15 minutes = 3800 feet
- Distance covered = 8000 - 3800 = 4200 feet
- Bryan's speed = Distance covered / Time = 4200 feet / 15 minutes = 280 feet per minute.
3. Comparing their speeds:
- Brendon’s speed: 270 feet per minute
- Bryan’s speed: 280 feet per minute
- Bryan walks faster than Brendon.
4. Initial distances from home:
- Brendon's initial distance: 7920 feet
- Bryan's initial distance: 8000 feet
- Bryan was farther away from home when he started walking.
Based on these calculations, let's now determine which statements are true:
- Brendon walks faster: This is false. Bryan walks faster because his speed is greater.
- Bryan walks faster: This is true. Bryan's speed is 280 feet per minute, which is faster than Brendon's 270 feet per minute.
- Brendon and Bryan walk at the same speed: This is false. Their speeds are different.
- Brendon was farther away from home when he started walking: This is false. Brendon started at 7920 feet, which is less than Bryan's 8000 feet.
- Bryan was farther away from home when he started walking: This is true. Bryan started at 8000 feet, which is more than Brendon's 7920 feet.
- Brendon and Bryan were an equal distance from home when they started walking: This is false. They started from different distances.
So, the correct statements are:
1. Bryan walks faster.
2. Bryan was farther away from home when he started walking.
