Question

Two cars that are originally 316 miles apart start traveling toward one another at 9:00 a.m. until they meet. One car travels 50 miles per hour and the other travels 50 miles per hour, both with their cruise control on. Which formula represents d , the distance between the two cars t hours after 9:00 a.m.?​

Answer 1

The formula to calculate the distance between two cars traveling toward each other at 50 miles per hour each, starting 316 miles apart, is d = 316 - 100t, where d represents the distance and t represents the time in hours after 9:00 a.m.

Step-by-step explanation:

To find the distance d, between two cars t hours after 9:00 a.m. when they start at 316 miles apart and travel toward each other at the same speed of 50 miles per hour each, we can use the concept of relative velocity.

Since both cars are moving towards each other, we effectively add their speeds together.

Thus the combined speed at which the distance between them is decreasing is

50 mph + 50 mph = 100 miles per hour.

The formula to calculate the remaining distance d between the two cars after t hours is:

d = Initial distance - (combined speed * time)

d = 316 miles - (100 mph * t)

Therefore, the formula representing the distance d, between the two cars t hours after 9:00 a.m. is:

d = 316 - 100t