Question

athy and Diane speed walk for exercise. Kathy walks at 4 mph while Diane walks at 5 mph. They stand and talk at a corner, then Diane starts walking east and Kathy starts walking north. Which choice is closest to the distance between them after 90 minutes? Hint: Distance rate time

Answer 1

To find the distance between Kathy and Diane after 90 minutes, you can use the formula:

Distance = Rate × Time

First, calculate the distance each of them has traveled in 90 minutes:

For Kathy (walking north):
Distance_Kathy = Rate_Kathy × Time = 4 mph × (90 minutes / 60 minutes per hour) = 6 miles

For Diane (walking east):
Distance_Diane = Rate_Diane × Time = 5 mph × (90 minutes / 60 minutes per hour) = 7.5 miles

Now, you can use the Pythagorean theorem to find the distance between them, as they've formed a right triangle with their paths:

Distance^2 = (Distance_Kathy)^2 + (Distance_Diane)^2

Distance^2 = (6 miles)^2 + (7.5 miles)^2
Distance^2 = 36 square miles + 56.25 square miles
Distance^2 = 92.25 square miles

Now, take the square root to find the distance:

Distance ≈ √92.25 ≈ 9.61 miles

So, the distance between Kathy and Diane after 90 minutes is closest to 9.61 miles.