Question

 A hiker is walking down a mountain. She walked​ 5,978 feet in 17 minutes. In that​ time, she descended​ 1,024 feet from the top of the mountain. She then walked​ 3,972 feet in 7 minutes. In that​ time, she descended 500 more feet. Express the average rate of change in altitude of the hiker from her starting point to her ending point as a unit rate.

Answer 1

first walk=descend of 1024 feet in 17 minutes
second walk=descend of 500 feet in 7 minutes

so in total she descended 1024+500=1524 feet in 7+17=24 minutes
as an average rate this equals 1524/24=63.5 feet/minute descended
or an average rate of -63.5 feet/minute in altitude (note the minus)

Answer 2

The average rate of change in altitude of the hiker from her starting point to her ending point is -63.5 feet per minute.

The following can be deduced based on the information provided in the question:

During the first walk, she descended 1024 feet and during the second walk, she descended 500 feet. Therefore, the total will be:

= 1024 feet + 500 feet = 1524 feet

During the first walk, the time taken was 17 minutes while for the second walk, the time taken was 7 minutes. Therefore, the total time taken will be:

= 17 minutes + 7 minutes

= 24 minutes.

Therefore, the average rate will be:

= 1524 / 24

= 63.5 feet per minute

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