Final answer:
The bicyclist is traveling at a rate of 8 miles per hour, which can be determined by dividing the distance by the time for each scenario provided. The equation representing the situation is r = d / t. None of the answer choices (a-d) are correct.
Step-by-step explanation:
The question asks us to find the rate at which a bicyclist is traveling, given that they traveled 16 miles in 2 hours and 48 miles in 6 hours. Since the relationship between the distance traveled and the time spent biking is proportional, we can use the formula for rate (speed), which is:
Rate = Distance / Time
For the first scenario:
- Distance = 16 miles
- Time = 2 hours
- Rate = 16 miles / 2 hours = 8 miles per hour
For the second scenario:
- Distance = 48 miles
- Time = 6 hours
- Rate = 48 miles / 6 hours = 8 miles per hour
Since the rate is the same in both cases, we confirm that the relationship is proportional. Thus, the bicyclist is traveling at a rate of 8 miles per hour. An equation that represents this situation is:
r = d / t
where 'r' is the rate, 'd' is the distance, and 't' is the time. Given the choices provided, none of them are correct since the actual rate is 8 miles per hour.