Mike and Sandra leave the seashore at the same time. Mike drives northward at a rate of 55mph, while Sandra drives west at 65mph. Find how far apart they are after 3 hours to the nearest mile.
north 55*3
west 65 * 3
hypotenuse = 3 sqrt (65^2+55^2)
55*3=165
65*3=195
195-165=30
Tara, the legs are 90 degrees from each other
To find how far apart Mike and Sandra are after 3 hours, we can use the Pythagorean theorem because they are moving in perpendicular directions (north and west). The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's represent the distance Mike travels as d1 and the distance Sandra travels as d2. Since they both left at the same time, both their distances can be calculated using the formula: distance = speed x time.
For Mike, distance = 55mph x 3 hours = 165 miles.
For Sandra, distance = 65mph x 3 hours = 195 miles.
Now, we can apply the Pythagorean theorem:
Distance^2 = d1^2 + d2^2
Distance^2 = 165^2 + 195^2
Distance^2 = 27225 + 38025
Distance^2 = 65250
Taking the square root of both sides to find the distance:
Distance ≈ √65250
Distance ≈ 255.41 miles (rounded to the nearest mile)
Therefore, Mike and Sandra are approximately 255 miles apart after 3 hours.