A runners racecourse has a total distance of 10miles. Race officials want to mark the course every 275 yd with a flag, including one at the finish line. The starting line does not need a flag. How many flags are needed?
To find the number of flags needed, we can start by converting the total distance of the racecourse from miles to yards. Since there are 1760 yards in a mile, the racecourse is 10 * 1760 = <<10*1760=17600>>17600 yards long.
Next, we divide the total distance of the racecourse by the distance between each flag, including one at the finish line. There are 275 + 1 = <<275+1=276>>276 yards between each flag, including one at the finish line.
Therefore, the number of flags needed is 17600 / 276 = <<17600/276=63.768>>63.768.
Since we cannot have a fraction of a flag, we round up to the nearest whole number.
Thus, 64 flags are needed. Answer: \boxed{64}.