Answer :
To find out how long it will take Joe to run a 10-mile race, we can follow a step-by-step approach:
1. Understand Joe's Running Rate:
- Joe ran 1.5 miles in 12 minutes. To find his running rate, we need to determine how many minutes it takes him to run 1 mile.
- To do this, divide the time he took by the distance he ran: [tex]\( \text{Rate} = \frac{12 \text{ minutes}}{1.5 \text{ miles}} \)[/tex].
- This calculation gives us Joe's running rate in minutes per mile.
2. Calculate Joe's Running Rate:
- [tex]\( \text{Rate} = \frac{12}{1.5} \)[/tex].
- This means Joe runs at a rate of 8 minutes per mile.
3. Determine the Time for 10 Miles:
- Joe's rate is 8 minutes per mile, and he needs to run 10 miles.
- To find the total time, multiply the rate (minutes per mile) by the total distance (miles): [tex]\( \text{Total Time} = 8 \text{ minutes/mile} \times 10 \text{ miles} \)[/tex].
4. Calculate the Total Time:
- [tex]\( \text{Total Time} = 80 \text{ minutes} \)[/tex].
Therefore, it will take Joe 80 minutes to run a 10-mile race. The correct answer is B: 80 minutes.
1. Understand Joe's Running Rate:
- Joe ran 1.5 miles in 12 minutes. To find his running rate, we need to determine how many minutes it takes him to run 1 mile.
- To do this, divide the time he took by the distance he ran: [tex]\( \text{Rate} = \frac{12 \text{ minutes}}{1.5 \text{ miles}} \)[/tex].
- This calculation gives us Joe's running rate in minutes per mile.
2. Calculate Joe's Running Rate:
- [tex]\( \text{Rate} = \frac{12}{1.5} \)[/tex].
- This means Joe runs at a rate of 8 minutes per mile.
3. Determine the Time for 10 Miles:
- Joe's rate is 8 minutes per mile, and he needs to run 10 miles.
- To find the total time, multiply the rate (minutes per mile) by the total distance (miles): [tex]\( \text{Total Time} = 8 \text{ minutes/mile} \times 10 \text{ miles} \)[/tex].
4. Calculate the Total Time:
- [tex]\( \text{Total Time} = 80 \text{ minutes} \)[/tex].
Therefore, it will take Joe 80 minutes to run a 10-mile race. The correct answer is B: 80 minutes.
