A scuba diver dove from the surface of the ocean to an elevation of −89
9
10
feet at a rate of −24 feet per minute. After spending 11.75 minutes at that elevation, the diver ascended to an elevation of −8
9
10
feet. The total time for the dive so far was 18
1
8
minutes. What was the rate of change in the diver's elevation during the ascent? Round your answer to the nearest hundredth.
To find the rate of change in the diver's elevation during the ascent, we need to calculate the difference in the elevations and divide it by the time taken for the ascent.
First, let's calculate the difference in the elevations:
Elevation at the start of the ascent = 89 9/10 feet
Elevation at the end of the ascent = -8 9/10 feet
To find the difference, we subtract the initial elevation from the final elevation:
Difference in elevations = Elevation at the end of the ascent - Elevation at the start of the ascent
Difference in elevations = (-8 9/10) - (89 9/10)
Difference in elevations = -8 9/10 - 89 9/10
Difference in elevations = -98 9/10
Next, let's calculate the time taken for the ascent:
Total time for the dive = 18 1/8 minutes
Time spent at the initial elevation = 11.75 minutes
To find the time taken for the ascent, we subtract the time spent at the initial elevation from the total dive time:
Time taken for the ascent = Total time for the dive - Time spent at the initial elevation
Time taken for the ascent = 18 1/8 - 11.75
Time taken for the ascent = 6 3/8
Now, to find the rate of change in the diver's elevation during the ascent, we divide the difference in elevations by the time taken for the ascent:
Rate of change = Difference in elevations / Time taken for the ascent
Rate of change = (-98 9/10) / (6 3/8)
To divide a mixed number by a mixed number, we first convert them into improper fractions:
Rate of change = (-989/10) / (51/8)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
Rate of change = (-989/10) * (8/51)
Rate of change = -7944/510
Now we round the rate of change to the nearest hundredth:
Rate of change ≈ -15.56
Therefore, the rate of change in the diver's elevation during the ascent is approximately -15.56 feet per minute.