Question

A rock climber is planning to climb a mountain cliff over two days. The climb begins at an altitude of 6,400 feet above sea level. The rock climber figures

he can climb at an average pace of 360 feet per hour. He wants to climb to an altitude higher than 8,020 feet above sea level by the end of the first day of
climbing.
Which inequality and solution describe how many hours the climber must climb on the first day to reach his goal?
A
360h + 6,400 < 8,020, with a solution of h < 4
2
B
360h + 6,400 < 8,020, with a solution of h < 7
71
C
360h + 6,400 > 8,020, with a solution of h > 75
18
D
360h + 6,400 > 8,020, with a solution of h > 4.
2

Answer 1

D

Explanation:

360h+6,400 >8,020, with a solution is h> 4.

Answer 2

The correct inequality to represent the climber's goal of exceeding 8,020 feet by the end of the first day is 360h + 6,400 > 8,020. After solving the inequality, we find that the climber must climb for more than 4.5 hours to reach his goal, making Option D the correct choice. therefore, option D is correct

The rock climber wants to climb to an altitude higher than 8,020 feet above sea level by the end of the first day, starting from 6,400 feet. Thus, we need an inequality that represents the climber's altitude after climbing for h hours at a pace of 360 feet per hour. Our inequality would look like this:

360h + 6,400 > 8,020.

This means the climber's total altitude after h hours must be greater than 8,020 feet. Now, let's solve for h to find out how many hours the climber needs to achieve this.

360h > 8,020 - 6,400
360h > 1,620
h > 1,620 / 360
h > 4.5

The climber needs to climb for more than 4.5 hours to exceed 8,020 feet. Therefore, the correct inequality and solution are:

Option D: 360h + 6,400 > 8,020, with a solution of h > 4.5.