Question

2.2
score: 21/23 answered: 22/23
question 23
two people are starting at the same road intersection. one drives directly east 45 miles per hour. the other drives directly north at 24 miles per hour. how far apart will they be from each other after half an hour? answer exactly, do not round.

miles
question help: written example

Explanation:

Step1: Calculate the distance each person travels

The person driving east travels at a speed of 45 miles per hour. In half - hour, the distance $d_1$ they travel is given by the formula $d = vt$, where $v = 45$ mph and $t=\frac{1}{2}$ hour. So $d_1=45\times\frac{1}{2}=\frac{45}{2}$ miles. The person driving north travels at a speed of 24 miles per hour. In half - hour, the distance $d_2$ they travel is $d_2 = 24\times\frac{1}{2}=12$ miles.

Step2: Use the Pythagorean theorem

Since their paths are perpendicular (east and north), the distance $D$ between them is the hypotenuse of a right - triangle with legs $d_1$ and $d_2$. By the Pythagorean theorem $D=\sqrt{d_1^{2}+d_2^{2}}$. Substitute $d_1=\frac{45}{2}$ and $d_2 = 12$ into the formula: $D=\sqrt{(\frac{45}{2})^{2}+12^{2}}=\sqrt{\frac{2025}{4}+144}=\sqrt{\frac{2025 + 576}{4}}=\sqrt{\frac{2601}{4}}=\frac{51}{2}$ miles.

Answer:

$\frac{51}{2}$