Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
One day at 3:00 a.m., the temperature was
–
13
°
F
in Kodiak, Alaska. At 10:00 a.m., the temperature was 22°F. What was the average change in temperature per hour?
We can start by finding the total change in temperature:
22°F - (-13°F) = 35°F
This is the change in temperature over 7 hours (from 3:00 a.m. to 10:00 a.m.). So to find the average change per hour, we can divide by 7:
35°F ÷ 7 hours = 5°F/hour
Therefore, the average change in temperature per hour is 5°F.
A mountain climber on Mt. Everest is at 29,035 ft above sea level. A stone at the bottom of the Dead Sea is at 1,349 ft below sea level. What is the difference in elevation between the mountain climber and the stone?
To find the difference in elevation, we need to subtract the altitude of the stone from the altitude of the mountain climber:
29,035 ft - (-1,349 ft) = 29,035 ft + 1,349 ft
When we add a negative number (subtracting a negative), we can simplify this by just adding the two positive numbers:
29,035 ft + 1,349 ft = 30,384 ft
Therefore, the difference in elevation between the mountain climber and the stone is 30,384 ft.
A deep-sea diver must descend and ascend in short steps to equalize pressure on his body. If the diver rises toward the surface too fast, he may suffer from a physical condition called “the bends.” Suppose the diver started at 82 feet below the surface and rose in five steps of 15 feet each. Use an integer to describe his new position in relation to the water surface.
••
If the diver started 82 feet below the surface and rose in five steps of 15 feet each, then the total rise would be:
5 steps x 15 feet/step = 75 feet
To find the diver's new position in relation to the water surface, we need to add the total rise to the starting depth:
82 feet + 75 feet = 157 feet
Therefore, the integer that describes the diver's new position in relation to the water surface is -157 feet. The negative sign indicates that the diver is still below the water surface.
An elevator on the 10th floor goes down 9 floors. Then it goes up 19 floors, down 3, and finally down 12. What floor does it end up on? Write an equation to show how you found your answer.
To find the floor the elevator ends up on, we can start with the 10th floor and then follow the sequence of movements:
10 - 9 = 1
1 + 19 = 20
20 - 3 = 17
17 - 12 = 5
Therefore, the elevator ends up on the 5th floor.
We can also write this using an equation:
10 - 9 + 19 - 3 - 12 = 5
Where:
- 10 is the starting floor
- Subtracting 9 floors takes the elevator down 9 floors
- Adding 19 floors takes the elevator up 19 floors
- Subtracting 3 floors takes the elevator down 3 floors
- Subtracting 12 floors takes the elevator down 12 more floors
- The final result 5 is the floor the elevator ends up on.