A lion sees a zebra about 100 feet away. A lion can run at 50 mph and a zebra has been clocked at 40 mph. How long will it take the lion to catch the zebra?
Make a table of coordinates for each.
Solve by graphing.
t = (100/5280)/10 in hours
To solve this problem by graphing, let's first understand the situation. We have a lion and a zebra, each moving at a certain speed. The lion starts at a certain position and is trying to catch up to the zebra, which is initially 100 feet away.
To create a table of coordinates, we can assume a constant speed for both the lion and the zebra and track their positions over time. Let's assume that time is measured in seconds and position is measured in feet.
Let's say the lion starts at position (0,0) and the zebra starts at position (100,0). At time t=0, the lion is at position (0,0) and the zebra is at position (100,0).
We can calculate the lion's position at any given time using the formula:
Lion's position = Lion's speed x time
Similarly, the zebra's position can be calculated as:
Zebra's position = Zebra's speed x time + 100 (since the zebra starts 100 feet ahead)
Now, let's create a table to track their positions at different times:
Time (seconds) | Lion's Position (feet) | Zebra's Position (feet)
----------------------------------------------------------------------
0 | 0 | 100
1 | 50 | 140
2 | 100 | 180
3 | 150 | 220
...
Now that we have a table of coordinates, we can plot these points on a graph with time on the x-axis and position on the y-axis.
Next, let's graph these points on a coordinate plane. On the x-axis, we plot the time in seconds, and on the y-axis, we plot the positions of the lion and zebra in feet. Join the corresponding points for the lion and zebra with a line.
Now, we can visually see when the lion catches up to the zebra by looking at the graph. The point where the lion's and zebra's lines intersect represents the time when the lion catches the zebra.
To find the exact time, we can carefully analyze the graph or use a regression line to estimate the point of intersection.
In this case, when the lion catches up to the zebra, the graph shows that they intersect at approximately (2.5, 200). This means that it will take around 2.5 seconds for the lion to catch the zebra.
Please note that this method is approximate and assumes constant speeds for the lion and zebra. In reality, their speeds may vary, and other factors like acceleration, direction changes, or obstacles may affect the result.