(a) To graph the information provided, you can plot the distance from home (in miles) against the time (in minutes).
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From 0 to 15 minutes: Andrew travels at a constant speed and covers 4 miles. This means he travels at a speed of 4 miles in 15 minutes, which is equivalent to \( \frac{4}{15} \) miles per minute. This will be a straight line from the point (0, 0) to the point (15, 4).
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From 15 to 25 minutes: Andrew rests for 10 minutes, so the distance remains constant at 4 miles. This will be a horizontal line from the point (15, 4) to the point (25, 4).
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From 25 to 45 minutes: Andrew rides his bike home for 20 minutes. Since he is returning back to 0 miles, he would cover 4 miles in 20 minutes, which gives him a speed of \( \frac{4}{20} = \frac{1}{5} \) miles per minute. This will be a straight line going down from the point (25, 4) to the point (45, 0).
You can plot these points on a graph with minutes on the x-axis and distance from home on the y-axis.
(b) To find Andrew's average speed on his way home, we determine the distance he traveled and the time it took to travel that distance.
- Distance: 4 miles (from 4 miles back to home)
- Time: 20 minutes
Average speed is calculated using the formula:
\[ \text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{4 \text{ miles}}{20 \text{ minutes}} = \frac{1}{5} \text{ miles per minute} = 0.2 \text{ miles per minute} \]
Thus, Andrew's average speed on his way home was 0.2 miles per minute.