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Brendon is walking home from a place that is 1.5 miles away. The function [tex]$y=7{,}920-270x$[/tex] represents Brendon's distance in feet from home, [tex]$y$[/tex], in relation to the number of minutes he walks, [tex]$x$[/tex]. Bryan is also walking home. Every 15 minutes, he writes down the number of feet left to reach home, as shown in the table below.

\begin{tabular}{|c|c|}
\hline
Minutes & Feet \\
\hline
0 & 8{,}000 \\
\hline
15 & 3{,}800 \\
\hline
\end{tabular}

Which statements about this situation are true?

A. Brendon walks faster.
B. Bryan walks faster.
C. Brendon and Bryan walk at the same speed.
D. Brendon was farther away from home when he started walking.
E. Bryan was farther away from home when he started walking.
F. Brendon and Bryan were an equal distance from home when they started walking.

Sagot :

GinnyAnsweridn
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.
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