i need to write this algabraically and graph: a runner leaves his house and runs for 30 minutes at 8mph, he rests for 5 minutes and then continues to run home at 5mph.
graph what?
speed?
position?
time?
i need to graph to show the runners distance in time
i need figure out the max distance from home ..i got that ,its 4 miles and its 48 minutes to get home after he stops the 5 min rest. what i am having problems with is graphing correctly with slope ..etc
To write this situation algebraically, let's first break it down into different parts:
1. The runner runs for 30 minutes at 8 mph.
2. Then, the runner rests for 5 minutes.
3. Finally, the runner continues to run home at 5 mph.
Let's denote the distance from the runner's house with the variable "x".
1. The distance the runner covers in the first part (30 minutes at 8 mph) can be calculated using the formula:
Distance = Time * Speed
Therefore, the distance for the first part is: (30/60) * 8 = 4x/3
2. For the resting period of 5 minutes, the runner's distance does not change, so it remains at 4x/3.
3. In the final part, the runner runs home at 5 mph. The time for this part can be calculated by subtracting the time already spent from 30 minutes:
Time = Total time - Time spent in the first part - Resting time
Time = 30 - 30/60 - 5 = 22.5 minutes or 22.5/60 hours
Now, let's find the distance the runner covers in the final part:
Distance = Time * Speed
Distance = (22.5/60) * 5 = 22.5x/60
To find the total distance covered, we need to add the distances of both parts:
Total Distance = Distance in the first part + Distance in the final part
Total Distance = 4x/3 + 22.5x/60
Simplifying this expression:
Total Distance = (20x + 22.5x)/60
Total Distance = 42.5x/60
Total Distance = 17x/24
To graph this situation, you can plot the total distance (y-axis) against time (x-axis). The x-values will correspond to the time elapsed, and the y-values will represent the total distance covered by the runner at that time.