Question

From a train station, one train heads north and another heads east. Some time later, the northbound train has traveled 64 kilometers. If the two trains separated by a straight-line distance of 80 kilometers, how far has the eastbound train traveled?

Answer 1

Answer: the eastbound train has traveled 48 kilometers.

Step-by-step explanation: Let’s solve this problem. We can imagine the two trains starting at the origin of a coordinate plane, with the northbound train traveling along the y-axis and the eastbound train traveling along the x-axis. The northbound train has traveled 64 kilometers, so its position is (0, 64). The eastbound train has traveled some distance x along the x-axis, so its position is (x, 0).

The straight-line distance between the two trains is given by the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). Plugging in the coordinates of the two trains and the given distance of 80 kilometers, we get: 80 = sqrt((x - 0)^2 + (0 - 64)^2). Squaring both sides and simplifying, we get: 6400 = x^2 + 4096. Solving for x, we get: x^2 = 2304. Taking the square root of both sides, we get: x = sqrt(2304) = 48.

So, the eastbound train has traveled 48 kilometers.