Square running tracks

Transcript

Square running tracksIn races, usually there is a common finish line for all the runners. Here are two square running tracks with the inner track of 100 m each side and outer track of 150 m each side. The common finishing line for both runners is shown by the flags in the figure which are in the center of one of the sides of the tracks. If the total race is of 350 m, then we have to find out where the starting positions of the two runners should be on these two tracks so that they both have a common finishing line after they run for 350 m. Mark the starting points of the runner on the inner track as ‘A’ and the runner on the outer track as ‘B’. Inner track To find the starting point, we trace back 350 m from the finish line (moving clockwise, opposite to the race direction shown by arrows). From the finish line to the bottom-left corner is 50 m. Outer track To find the starting point, we trace back 350 m from the finish line (moving clockwise, opposite to the race direction shown by arrows). From the bottom-left corner, we trace back the remaining 300 m (350−50). This path goes up the left side (100 m), across the top (100 m), and down the right side (100 m). This 300 m trace ends exactly at the bottom-right corner. From the finish line to the bottom-left corner is 75 m. The remaining distance to trace back is 350 m−75 m=275 m. From the bottom-left corner, tracing up the left side uses 150 m. The final remaining distance is 275 m−150 m = 125 m. This distance is measured clockwise along the top side from the top-left corner.