Question

find veda and Caleb's climbing speeds.
veda's speed: ___ per minute
caleb's speed: ___ per minute

veda's hike: y = 10x + 600

caleb's hike: minutes, x elevation,y
1 570
2 550
3 530
4 510

Answer 1

To find Veda and Caleb's climbing speeds, we need to analyze the provided equations and data.

**Veda's Climbing Speed:**
Veda's hike is represented by the equation \(y = 10x + 600\).

In this equation, \(y\) represents the elevation (in meters), and \(x\) represents the time (in minutes).

From this equation, we can deduce Veda's climbing speed. The coefficient of \(x\) (which is 10) represents the rate of change of elevation with respect to time, meaning Veda climbs at a speed of **10 meters per minute**.

**Caleb's Climbing Speed:**
Next, we look at Caleb's hike data:

| Minutes (x) | Elevation (y) |
|:--------------:|:-------------:|
| 1 | 570 |
| 2 | 550 |
| 3 | 530 |
| 4 | 510 |

To find Caleb's speed, we can calculate the change in elevation over time between consecutive minutes.

- From minute 1 to minute 2:
- Elevation change: \(550 - 570 = -20\) meters
- Time taken: \(2 - 1 = 1\) minute
- Speed: \(-20 / 1 = -20\) meters per minute

- From minute 2 to minute 3:
- Elevation change: \(530 - 550 = -20\) meters
- Time taken: \(3 - 2 = 1\) minute
- Speed: \(-20 / 1 = -20\) meters per minute

- From minute 3 to minute 4:
- Elevation change: \(510 - 530 = -20\) meters
- Time taken: \(4 - 3 = 1\) minute
- Speed: \(-20 / 1 = -20\) meters per minute

Caleb's speed is consistently **-20 meters per minute**, which indicates he is descending.

So, in summary:
- Veda's climbing speed: **10 meters per minute**
- Caleb's climbing speed: **-20 meters per minute** (descending).