Question

Two families leave their homes at the same time to meet for lunch. The families live 210 miles apart, and one family drives 5 mph slower than the other. If it takes them 2 hours to meet at a point between their homes, how fast does each family travel?

a. The first family drives at 60 mph, and the second family drives at 55 mph.
b. The first family drives at 55 mph, and the second family drives at 60 mph.
c. The first family drives at 65 mph, and the second family drives at 60 mph.
d. The first family drives at 60 mph, and the second family drives at 65 mph.

Answer 1

To solve this problem, we can set up an equation using the formula speed = distance/time. The faster family drives at 107.5 mph, and the slower family drives at 102.5 mph.

Step-by-step explanation:

To solve this problem, we can set up an equation using the formula speed = distance/time. Let's assume that the faster family drives at a rate of x mph. Then the slower family drives at a rate of (x-5) mph. The distance between the two families is 210 miles. Since they meet in 2 hours, we can set up the equation:

(210/2) = (x + (x-5))/2

Simplifying this equation, we get:

210 = 2x - 5

Adding 5 to both sides, we get:

215 = 2x

Dividing both sides by 2, we get:

x = 107.5

Therefore, the faster family drives at 107.5 mph, and the slower family drives at (107.5 - 5) = 102.5 mph. So, the correct answer is:

b. The first family drives at 55 mph, and the second family drives at 60 mph.