The missing time is 9 minutes, and the distance after 20 minutes is unknown ("d" meters).
Based on the information given in the table, Heather recorded the time and distance she traveled during her hike. However, there are two incomplete entries in the table. Let's analyze the available data and see what we can conclude from it.
The first entry in the table states that after 4 minutes, Heather had traveled 200 meters. This gives us a speed of 200 meters in 4 minutes. To find the speed in meters per minute, we can divide the distance by the time: 200 meters / 4 minutes = 50 meters per minute.
The second entry tells us that at some point, Heather traveled a distance of 450 meters, but we don't know the corresponding time. Let's call this unknown time "t". Since we know the speed is 50 meters per minute, we can set up the following equation:
50 meters per minute × t minutes = 450 meters
By solving this equation, we can find the value of "t". Dividing both sides of the equation by 50 meters per minute gives us:
t minutes = 450 meters / 50 meters per minute
t minutes = 9 minutes
Therefore, the missing time is 9 minutes.
Moving on to the third entry, we see that after 14 minutes, Heather traveled 700 meters. Using the same logic as before, we can calculate the speed:
700 meters / 14 minutes = 50 meters per minute
This confirms that Heather's speed remained constant at 50 meters per minute.
Lastly, the fourth entry in the table states that after 20 minutes, Heather had traveled a distance of "d" meters. Since we don't know the value of "d", we can't calculate the speed or determine any specific distance. However, we do know that the speed remains constant at 50 meters per minute based on the previous calculations.