| I tried this: > Solve the following word problem step by step: > "John is in a train moving west at ten miles per hour. Jill is in a train moving north at twenty miles per hour. How fast are John and Jill moving apart from each other?" To solve this problem, we first need to understand the concept of speed. Speed is a measure of distance traveled over time. In this problem, we are told that John and Jill are traveling at different speeds in different directions. Since the two trains are moving in different directions, we cannot simply add or subtract their speeds to find the combined speed at which John and Jill are moving apart from each other. Instead, we need to use the Pythagorean theorem to find the combined speed. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the lengths of the other two sides. In this problem, we can consider the trains to be moving along the two sides of a right triangle, with the distance between them as the hypotenuse. We can use the Pythagorean theorem to find the distance between John and Jill as follows: First, we square the speed of each train and add the results: 10 mph * 10 mph + 20 mph * 20 mph = 100 + 400 = 500 Next, we take the square root of the result to find the distance between John and Jill: sqrt(500) = 22.36 mph Therefore, the combined speed at which John and Jill are moving apart from each other is approximately 22.36 mph. --- Results seem pretty inconsistent though. Other attempts have given complete nonsense. |