Questions: Two cars start moving from the same point. One travels south at 20 mi / h and the other travels west at 15 mi / h. At what rate (in mi/h) is the distance between the cars increasing three hours later?

Two cars start moving from the same point. One travels south at 20 mi / h and the other travels west at 15 mi / h. At what rate (in mi/h) is the distance between the cars increasing three hours later?

Transcript text: Two cars start moving from the same point. One travels south at $20 \mathrm{mi} / \mathrm{h}$ and the other travels west at $15 \mathrm{mi} / \mathrm{h}$. At what rate (in mi/h) is the distance between the cars increasing three hours later?

Solution

Solution Steps

Step 1: Identify the speeds and directions of the cars

Car 1 travels south at 20 mi/h.
Car 2 travels west at 15 mi/h.

Step 2: Calculate the distances traveled by each car after 3 hours

Distance traveled by Car 1: $ 20 \text{ mi/h} \times 3 \text{ h} = 60 \text{ mi} $
Distance traveled by Car 2: $ 15 \text{ mi/h} \times 3 \text{ h} = 45 \text{ mi} $

Step 3: Use the Pythagorean theorem to find the distance between the cars