Questions: A swim race has a total distance of 22.5 mi . Race officials want to mark the course every 600 yd with a buoy, including one at the finish line. (The starting line does not need a buoy.) How many buoys are needed? First fill in the blanks on the left side of the equation using three of the ratios shown. Then write your answer on the right side of the equation.

A swim race has a total distance of 22.5 mi . Race officials want to mark the course every 600 yd with a buoy, including one at the finish line. (The starting line does not need a buoy.) How many buoys are needed?
First fill in the blanks on the left side of the equation using three of the ratios shown. Then write your answer on the right side of the equation.

Transcript text: A swim race has a total distance of 22.5 mi . Race officials want to mark the course every 600 yd with a buoy, including one at the finish line. (The starting line does not need a buoy.) How many buoys are needed? First fill in the blanks on the left side of the equation using three of the ratios shown. Then write your answer on the right side of the equation.

Solution

Solution Steps

Step 1: Convert the total distance from miles to yards

To convert the distance from miles to yards, multiply the distance in miles (22.5 miles) by the conversion factor (1760 yards/mile). Distance in yards = 22.5 miles * 1760 yards/mile = 39600 yards.

Step 2: Calculate the number of buoys needed

Divide the total distance in yards (39600 yards) by the interval between buoys (600 yards) to determine how many intervals fit into the total distance. Number of buoys needed (excluding rounding) = 39600 yards / 600 yards = 66 buoys.

Step 3: Round up to ensure a buoy at the finish line

Since the total distance divided by the interval might leave a remainder, we round up to the next whole number to ensure a buoy is placed at the finish line. Total number of buoys needed = 66 buoys.