Question

Two people start at Walmart. John begins heading west at a rate of 60 mph. After 30 minutes, Chase begins heading North at a rate of 55 mph. How is the distance between them changing after 3 hours, after Chase begins traveling?

a) It is increasing
b) It is decreasing
c) It is constant
d) It is not possible to determine with the given information.

Answer 1

The distance between John and Chase is decreasing after 3 hours.

Step-by-step explanation:

To find out how the distance between John and Chase is changing after 3 hours, we need to determine their positions at that time. Since John started 30 minutes earlier and travels at a constant speed of 60 mph, he would have covered a distance of 60 miles in 3 hours. Chase, on the other hand, started after 30 minutes and travels at a constant speed of 55 mph. So after 3 hours, Chase would have covered a distance of 55 * (3 - 0.5) = 137.5 miles.

To find the distance between them, we can use the Pythagorean theorem since they are moving in perpendicular directions. The distance between them is √[(60^2) + (137.5^2)] = √(3600 + 18906.25) = √22506.25 = 150.09 miles.

Now let's see how this distance is changing. Since John is traveling west and Chase is traveling north, the distance between them is decreasing. This is because their velocities are opposite in directions. Thus, the correct answer is b) It is decreasing.