Question

craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average speed of 20 miles per hour. the entire two - part, 15 - mile race took him 1.125 hours to complete. which table correctly represents his rates, times, and distances for each part of the race?

	rate (mi/h)	time (h)	distance (mi)
bike	20	15 - t	20(15 - t)

	rate (mi/h)	time (h)	distance (mi)
bike	\\(\frac{1}{20}\\)	15 - t	\\(\frac{1}{20}(15 - t)\\)

	rate (mi/h)	time (h)	distance (mi)
bike	20	1.125 - t	20(1.125 - t)

Explanation:

Step1: Recall the formula for distance

The formula for distance is \( \text{Distance} = \text{Rate} \times \text{Time} \), or \( d = rt \). Also, the total time for the race is the sum of the time spent running and the time spent biking. The total time is \( 1.125 \) hours, and the total distance is \( 15 \) miles.

Step2: Analyze the time for each part

Let \( t \) be the time (in hours) spent running. Then the time spent biking should be the total time minus the running time, which is \( 1.125 - t \) hours (since total time is \( 1.125 \) hours).

Step3: Analyze the rate and distance for each part

• For running: The rate is \( 8 \) miles per hour, time is \( t \) hours, so distance is \( 8t \) miles (using \( d = rt \)).
• For biking: The rate is \( 20 \) miles per hour, time is \( 1.125 - t \) hours, so distance is \( 20(1.125 - t) \) miles.

Now let's check the three tables:

• First table: The time for biking is given as \( 15 - t \), which is incorrect because \( 15 \) is the total distance, not total time.
• Second table: The rates are incorrect (they are the reciprocals of the speeds, which doesn't make sense for rate in distance - time context).
• Third table: Running rate is \( 8 \), time \( t \), distance \( 8t \); biking rate is \( 20 \), time \( 1.125 - t \), distance \( 20(1.125 - t) \). This follows the distance - rate - time formula and uses total time correctly.

Answer:

The third table (with Run: Rate = 8, Time = t, Distance = 8t; Bike: Rate = 20, Time = 1.125 - t, Distance = 20(1.125 - t))