Question

Nola hiked down a trail at a steady rate for 10 minutes. Her change in elevation was -200 feet. Then she continued to hike down for another 20 minutes at a different rate . Her change in elevation for this part of the hike -300 feet. During which portion of the hike did she walk down at a faster rate? Explain your reasoning

Answer 1

Answer:

1st portion

Step-by-step explanation:

Time taken for the 1st part of the hike = 10 minutes

Change in elevation in 1st part = - 200 feet

The negative sign indicates that the elevation is decreasing. So this means, elevation of Nola decreased by 200 feet in 10 minutes during this part.

We need to find out the rate i.e. the speed of her walk or hike. Since, speed is the ratio of distance to time, in this case it would be:

$\text{Rate}_{1}=\frac{\text{Change in Elevation}}{\text{Time Taken}}$

Using the values, we get:

$\text{Rate}_{1}=\frac{-200}{10}=-20$ feet per minute

This means during the 1st part her rate of walk was 20 feet per minute down the hill.

Time taken for the 2nd part of the hike = 20 minutes

Change in elevation in 2nd part = - 300 feet

Using the same formula we used above, we get:

$\text{Rate}_{2}=\frac{-300}{20}=-15$ feet per minute

This means during the 2nd part her rate of walk was 15 feet per minute down the hill.

Thus, Nola hiked down faster in the 1st portion of the hike.