Veda climbs up the mountain while Kaleb climbs down. The equation and the table represent the
elevations of the climbers in feet, y, as functions of time in minutes, .
Find Veda and Kaleb's climbing speeds.
>) Veda's speed=
Kaleb's speed=
feet per minute
? feet per minute
h
Veda's hike:
y = 10x + 600
Kaleb's hike:
Minutes,
1
2
3
4
Elevation, y
570
550
530
510
To find Veda's climbing speed, we need to determine the slope of her equation. The slope represents the rate at which her elevation changes with respect to time. In the equation y = 10x + 600, the coefficient of x, which is 10, represents the slope.
Therefore, Veda's climbing speed is 10 feet per minute.
To find Kaleb's climbing speed, we need to determine the slope of his table. The change in elevation (y) divided by the change in time (x) will give us Kaleb's climbing speed.
From the table, the change in elevation from 570 to 550 is -20 feet, and the corresponding change in time is 1 minute. Therefore, Kaleb's climbing speed from minutes 1 to 2 is -20 feet per minute.
From the table, the change in elevation from 550 to 530 is -20 feet, and the corresponding change in time is 1 minute. Therefore, Kaleb's climbing speed from minutes 2 to 3 is -20 feet per minute.
From the table, the change in elevation from 530 to 510 is -20 feet, and the corresponding change in time is 1 minute. Therefore, Kaleb's climbing speed from minutes 3 to 4 is -20 feet per minute.
Since the rate of change is constant for Kaleb, we can conclude that his climbing speed is -20 feet per minute.
Note: The negative sign for Kaleb's climbing speed indicates that he is climbing down the mountain. Hence, his speed is in the downward direction.
To find Veda's climbing speed, we need to determine the slope of the equation that represents her hike, y = 10x + 600. The slope represents how much the elevation changes over time.
Since the equation is in the form y = mx + b, where m is the slope, we can see that Veda's climbing speed is 10 feet per minute.
To find Kaleb's climbing speed, we need to determine the change in elevation over time from the table provided.
Let's calculate the difference in elevation between each minute:
- From minute 1 to minute 2, the change in elevation is 570 - 550 = 20 feet.
- From minute 2 to minute 3, the change in elevation is 550 - 530 = 20 feet.
- From minute 3 to minute 4, the change in elevation is 530 - 510 = 20 feet.
Since Kaleb's climbing speed represents the change in elevation per minute, we can see that his climbing speed is also 20 feet per minute.
Therefore, Veda's speed is 10 feet per minute, and Kaleb's speed is 20 feet per minute.
Well, it seems like Veda is climbing up the mountain, so her speed must be positive. On the other hand, Kaleb is climbing down, so his speed must be negative.
To find their speeds, we can compare their elevation changes to the time it takes. Let's check the table:
Veda's hike:
Yikes! It seems Veda's elevation is decreasing by 20 feet every 1 minute. Therefore, her speed is -20 feet per minute.
Kaleb's hike:
Oopsie! Kaleb's elevation is decreasing by 20 feet every 1 minute as well. So, Kaleb's speed is -20 feet per minute.
So, to summarize:
Veda's speed = -20 feet per minute.
Kaleb's speed = -20 feet per minute.
Keep in mind that these speeds are approximate values based on the given information. Just remember - they climb at the speed of a depressed snail!
Veda's speed = 10 feet per minute
Kaleb's speed = -20 feet per minute