Juan drives 7.5 miles in 15 minutes. If he drove three hours in total at the same rate, how far did he go? How many minutes did Juan drive in total?
The correct answer and explanation is:
Correct Answer:
- Juan drove 90 miles in total.
- Juan drove for 180 minutes in total.
Explanation:
To solve this problem, we first need to determine Juan’s speed in miles per minute.
- Determine Juan’s speed:
Juan drives 7.5 miles in 15 minutes. To find his speed in miles per minute, we divide the distance by the time. Speed=7.5 miles15 minutes=0.5 miles per minute\text{Speed} = \frac{7.5 \text{ miles}}{15 \text{ minutes}} = 0.5 \text{ miles per minute} This means Juan drives 0.5 miles every minute. - Calculate how far Juan drove in 3 hours:
Next, we need to calculate the total distance Juan drove in 3 hours. Since there are 60 minutes in an hour, 3 hours equals: 3 hours=3×60=180 minutes3 \text{ hours} = 3 \times 60 = 180 \text{ minutes} Now, to find the total distance driven, multiply Juan’s speed by the total time he drove: Distance=0.5 miles/minute×180 minutes=90 miles\text{Distance} = 0.5 \text{ miles/minute} \times 180 \text{ minutes} = 90 \text{ miles} Therefore, Juan drove a total of 90 miles in 3 hours. - Total time driven:
As calculated earlier, Juan drove for 180 minutes in total, which is equivalent to 3 hours.
Thus, by maintaining the same rate of 0.5 miles per minute, Juan traveled 90 miles in 180 minutes (or 3 hours).