To determine which equation represents Jay's situation, let’s break down the given information:
1. Jay walks at a speed of 3 miles per hour.
2. Jay runs at a speed of 5 miles per hour.
3. He walks for [tex]\( w \)[/tex] hours.
4. He runs for [tex]\( r \)[/tex] hours.
5. The combined distance for walking and running is 14 miles.
Now, let’s express the distances:
- The distance Jay walks is calculated by multiplying his walking speed by the time he spends walking, which is [tex]\( 3w \)[/tex] miles.
- The distance Jay runs is calculated by multiplying his running speed by the time he spends running, which is [tex]\( 5r \)[/tex] miles.
Given that the total distance covered is 14 miles, we can write the equation as:
[tex]\[ 3w + 5r = 14 \][/tex]
Now, compare this equation with the answer choices:
(A) [tex]\( 3w + 5r = 14 \)[/tex]
(B) [tex]\( \frac{1}{3}w + \frac{1}{5}r = 14 \)[/tex]
(C) [tex]\( \frac{1}{3}w + \frac{1}{5}r = 112 \)[/tex]
(D) [tex]\( 3w + 5r = 112 \)[/tex]
The correct equation that represents Jay's scenario is:
[tex]\[ 3w + 5r = 14 \][/tex]
Thus, the correct answer is:
(A) [tex]\( 3w + 5r = 14 \)[/tex]
