Question

A triangular course for a sailing race is marked off by buoys. The first leg is 250 meters longer than the second, and the third leg is 100 meters shorter than the first. If the length of the course is 2500 meters, find the length of each leg.

Answer 1

To solve for the lengths of the legs of the sailing race course, we assigned the length of the second leg as x meters and established equations based on the problem's conditions. Solving these equations gave us 700 meters for the second leg, 950 meters for the first leg, and 850 meters for the third leg.

Step-by-step explanation:

The subject of this question is a mathematical problem involving algebra and the solution of a system of equations. Here is how we can find the length of each leg of the triangular sailing race course:

1. Let's denote the second leg's length as x meters.
2. According to the information provided, the first leg is 250 meters longer than the second, so it's length would be x + 250 meters.
3. The third leg is 100 meters shorter than the first, therefore it's length is (x + 250) - 100 = x + 150 meters.
4. The total length of the course is given as 2500 meters, so we get the equation:
   x + (x + 250) + (x + 150) = 2500.
5. Simplified, the equation becomes 3x + 400 = 2500.
6. Subtract 400 from both sides to get 3x = 2100.
7. Divide by 3 to find x, which gives us x = 700 meters.
8. Plug in x to find the lengths of the other two legs: the first leg is 950 meters and the third leg is 850 meters.