Question

lesson 15 | session 23. an elevator in the seattle space needle can rise 100 meters in 50 seconds. use a model to show the elevators rate of travel in meters per second and in seconds per meter. describe each rate in words.the space needle is an observation tower in seattle, washington.4. zahara rides with her dad to her grandmothers house. they travel 159 miles in 3 hours. her uncle, jorge, drives there separately from his home.a. at what speed does zaharas dad drive, in miles per hour? draw a model to show your work.solutionb. jorges trip takes the same amount of time as zaharas, but he travels a shorter distance. does jorge drive faster or slower than zaharas dad?5. a store changes the cost of a package of batteries. now customers pay more money for the same number of batteries. did the cost per battery increase, decrease, or stay the same? explain how you know.

Explanation:

(Problem 3):

Step1: Calculate m/s rate

$\text{Rate (m/s)} = \frac{\text{Total distance}}{\text{Total time}} = \frac{100}{50} = 2$

Step2: Calculate seconds per meter

$\text{Rate (s/m)} = \frac{\text{Total time}}{\text{Total distance}} = \frac{50}{100} = 0.5$

Step3: Describe each rate

The first rate means the elevator rises 2 meters each second. The second rate means it takes 0.5 seconds to rise 1 meter.

(Problem 4a):

Step1: Calculate speed (mph)

$\text{Speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{159}{3} = 53$

Step2: Model explanation

A bar model can be drawn with 3 equal segments representing 3 hours, and the total length of the bar is 159 miles. Each segment (1 hour of travel) equals 53 miles.

(Problem 4b):

Step1: Relate speed, distance, time

Speed is calculated as $\frac{\text{distance}}{\text{time}}$. For equal time, speed is proportional to distance.

Step2: Compare speeds

Jorge travels a shorter distance in the same time, so his speed is lower.

(Problem 5):

Step1: Define cost per battery

$\text{Cost per battery} = \frac{\text{Total cost}}{\text{Number of batteries}}$

Step2: Analyze change

The number of batteries is constant, while total cost increases. A larger numerator with fixed denominator increases the value.

Answer:

(Problem 3):
The elevator's rate is 2 meters per second (it travels 2 meters every second) and 0.5 seconds per meter (it takes half a second to travel 1 meter).

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