Question
As part of an annual fundraiser to help raise money for cancer research, Christine joined a walkathon. The track she wa 770 yd long. Christine walked 16 laps. Her sponsors agreed to donate an amount of money for each mile she walked. H 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.
16 laps/1 x (?) x (?) x (?) = (? miles)
ratios: 5280 ft/1 mi, 1mi/5280 ft, 770yd/1 lap, 1 lap, 770 yd, 3ft/1 yd, 1yd/ 3ft
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.
16 laps/1 x (?) x (?) x (?) = (? miles)
ratios: 5280 ft/1 mi, 1mi/5280 ft, 770yd/1 lap, 1 lap, 770 yd, 3ft/1 yd, 1yd/ 3ft
Answers
GPT-4o mini
To find out how many miles Christine walked, we need to convert the total distance she walked from yards to miles. First, we calculate the total distance she walked in yards, and then convert that to miles.
**Step 1: Total distance walked in yards**
Christine walked 16 laps, and each lap is 770 yards.
Total distance in yards = 16 laps × 770 yards/lap = 12320 yards.
**Step 2: Convert yards to miles**
We need to convert 12320 yards to miles using the given ratios. We can use the following conversions:
- There are 3 feet in a yard (3 ft/1 yd).
- There are 5280 feet in a mile (5280 ft/1 mi).
We will fill in the blanks as follows:
**Fill in the blanks:**
16 laps/1 x (770 yd/1 lap) x (3 ft/1 yd) x (1 mi/5280 ft) = (?) miles.
**Step-by-step calculation:**
1. Start with 16 laps:
\( 16 \text{ laps} \)
2. Convert laps to yards:
\( 16 \text{ laps} \times 770 \text{ yd/lap} = 12320 \text{ yd} \)
3. Convert yards to feet:
\( 12320 \text{ yd} \times 3 \text{ ft/yd} = 36960 \text{ ft} \)
4. Convert feet to miles:
\( 36960 \text{ ft} \div 5280 \text{ ft/mi} = 7 \text{ miles} \)
**Final Result:**
Thus, Christine walked a total of 7 miles.
Finally, we can write the equation as follows:
16 laps/1 x (770 yd/1 lap) x (3 ft/1 yd) x (1 mi/5280 ft) = 7 miles.
**Step 1: Total distance walked in yards**
Christine walked 16 laps, and each lap is 770 yards.
Total distance in yards = 16 laps × 770 yards/lap = 12320 yards.
**Step 2: Convert yards to miles**
We need to convert 12320 yards to miles using the given ratios. We can use the following conversions:
- There are 3 feet in a yard (3 ft/1 yd).
- There are 5280 feet in a mile (5280 ft/1 mi).
We will fill in the blanks as follows:
**Fill in the blanks:**
16 laps/1 x (770 yd/1 lap) x (3 ft/1 yd) x (1 mi/5280 ft) = (?) miles.
**Step-by-step calculation:**
1. Start with 16 laps:
\( 16 \text{ laps} \)
2. Convert laps to yards:
\( 16 \text{ laps} \times 770 \text{ yd/lap} = 12320 \text{ yd} \)
3. Convert yards to feet:
\( 12320 \text{ yd} \times 3 \text{ ft/yd} = 36960 \text{ ft} \)
4. Convert feet to miles:
\( 36960 \text{ ft} \div 5280 \text{ ft/mi} = 7 \text{ miles} \)
**Final Result:**
Thus, Christine walked a total of 7 miles.
Finally, we can write the equation as follows:
16 laps/1 x (770 yd/1 lap) x (3 ft/1 yd) x (1 mi/5280 ft) = 7 miles.