Questions: As part of an annual fundraiser to help raise money for cancer research, Heather joined a walkathon. The track she walked on was 1600 yd long. Heather walked 16.5 laps. Her sponsors agreed to donate an amount of money for each mile she walked. How many miles did she walk? 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. Ratios: 5280 ft / 1 mi 1 mi / 5280 ft 1600 yd / 1 lap 1 lap / 1600 yd 3 ft / 1 yd - 1 yd / 3 ft ft yd mi in lap 16.5 laps / 1 × × × = miles

As part of an annual fundraiser to help raise money for cancer research, Heather joined a walkathon. The track she walked on was 1600 yd long. Heather walked 16.5 laps. Her sponsors agreed to donate an amount of money for each mile she walked. How many miles did she walk? 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. Ratios: 5280 ft / 1 mi 1 mi / 5280 ft 1600 yd / 1 lap 1 lap / 1600 yd 3 ft / 1 yd - 1 yd / 3 ft ft yd mi in lap 16.5 laps / 1 × × × = miles
Transcript text: As part of an annual fundraiser to help raise money for cancer research, Heather joined a walkathon. The track she walked on was 1600 yd long. Heather walked 16.5 laps. Her sponsors agreed to donate an amount of money for each mile she walked. How many miles did she walk? 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. Ratios: $\frac{5280 \mathrm{ft}}{1 \mathrm{mi}}$ $\frac{1 \mathrm{mi}}{5280 \mathrm{ft}}$ $\left.\frac{1600 \mathrm{yd}}{1 \text { lap }} \right\rvert\, \frac{1 \text { lap }}{1600 \mathrm{yd}}$ $\frac{3 \mathrm{ft}}{1 \mathrm{yd}}$ - $\frac{1 \mathrm{yd}}{3 \mathrm{ft}}$ ft yd mi in lap $\frac{16.5 \text { laps }}{1} \times$ $\square$ $\square$ $\square$ $=$ $\square$ miles
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Solution

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Solution Steps

To solve this problem, we need to convert the total distance Heather walked from yards to miles. First, calculate the total distance in yards by multiplying the number of laps by the length of the track in yards. Then, convert the distance from yards to feet using the conversion factor (1 yard = 3 feet). Finally, convert the distance from feet to miles using the conversion factor (5280 feet = 1 mile).

Step 1: Calculate Total Distance in Yards

To find the total distance Heather walked, we multiply the number of laps by the length of the track: \[ \text{Total Distance (yards)} = 16.5 \, \text{laps} \times 1600 \, \text{yards/lap} = 26400 \, \text{yards} \]

Step 2: Convert Yards to Feet

Next, we convert the total distance from yards to feet using the conversion factor \(1 \, \text{yard} = 3 \, \text{feet}\): \[ \text{Total Distance (feet)} = 26400 \, \text{yards} \times 3 \, \text{feet/yard} = 79200 \, \text{feet} \]

Step 3: Convert Feet to Miles

Finally, we convert the total distance from feet to miles using the conversion factor \(5280 \, \text{feet} = 1 \, \text{mile}\): \[ \text{Total Distance (miles)} = \frac{79200 \, \text{feet}}{5280 \, \text{feet/mile}} = 15.0 \, \text{miles} \]

Final Answer

The total distance Heather walked is \(\boxed{15.0 \, \text{miles}}\).

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