Question

date

1. jada was climbing down a mountain and into a cave at a constant rate. a photographer takes a picture of jada when she is at sea level. 10 minutes after the picture was taken, jada had climbed down 120 feet into the cave.

a. at what rate is jada climbing? use a signed number, and include the unit of measurement in your answer.
b. how many minutes will it take for jada to get to the bottom of the cave, which is at an elevation of -450 feet? explain or show your reasoning.
c. how many minutes before jada had her picture taken was she at an elevation of 280 feet? explain or show your reasoning.

Explanation:

Part (a)

Step1: Recall rate formula

Rate is calculated as change in distance over change in time. Here, distance (elevation change) is -120 feet (negative because she's climbing down) and time is 10 minutes.
$$\text{Rate} = \frac{\text{Change in Elevation}}{\text{Change in Time}}$$

Step2: Substitute values

Substitute change in elevation = -120 feet and change in time = 10 minutes.
$$\text{Rate} = \frac{-120}{10} = -12 \text{ feet per minute}$$

Step1: Recall time formula

Time is calculated as change in elevation divided by rate. The target elevation is -450 feet (starting from 0 at picture time), and rate is -12 feet per minute.
$$\text{Time} = \frac{\text{Target Elevation - Initial Elevation}}{\text{Rate}}$$

Step2: Substitute values

Initial elevation at picture time is 0, target is -450, rate is -12.
$$\text{Time} = \frac{-450 - 0}{-12} = \frac{-450}{-12} = 37.5 \text{ minutes}$$

Step1: Recall time formula

Time is change in elevation divided by rate. The elevation before picture is 280 feet (so change in elevation from 280 to 0 is -280), rate is -12 feet per minute.
$$\text{Time} = \frac{\text{Final Elevation - Initial Elevation}}{\text{Rate}}$$

Step2: Substitute values

Final elevation (at picture) is 0, initial is 280, rate is -12.
$$\text{Time} = \frac{0 - 280}{-12} = \frac{-280}{-12} = \frac{70}{3} \approx 23.33 \text{ minutes (or } 23\frac{1}{3} \text{ minutes)}$$

Answer:

-12 feet per minute

Part (b)