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A bicyclist travels 16 miles in 2 hours and 48 miles in 6 hours. If the number of miles traveled and the time spent biking is in a proportional linear relationship, at what rate is the bicyclist traveling? Write an equation that represents the situation.

A. 10 miles per hour
B. 12 miles per hour
C. 14 miles per hour
D. 16 miles per hour

Answer :

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.

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.

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Rewritten by : Barada