Question
The wind speed, y, (in miles per hour) of tropical storm Albert is y=2x+55, where x is the number of hours after the storm enters the Gulf of Mexico.
The wind speed, y, (in miles per hour) of tropical storm Betty is shown in the graph.
Use the image to answer the question.
The graph is labeled "Tropical Storm Betty". The y axis is labeled "Wind Speed (miles per hour)", and goes 0, 10 , 20, 30, 40, 50, 60, 70, 80, 90. The X axis is labeled "hours after entering the gulf" and goes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. It shows a line starting at (0, 40) and passes through (5, 60)
A tropical storm becomes a hurricane when wind speeds are at least 74 miles per hour.
If each storm follows their given pattern, which storm will become a hurricane first?
The wind speed, y, (in miles per hour) of tropical storm Betty is shown in the graph.
Use the image to answer the question.
The graph is labeled "Tropical Storm Betty". The y axis is labeled "Wind Speed (miles per hour)", and goes 0, 10 , 20, 30, 40, 50, 60, 70, 80, 90. The X axis is labeled "hours after entering the gulf" and goes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. It shows a line starting at (0, 40) and passes through (5, 60)
A tropical storm becomes a hurricane when wind speeds are at least 74 miles per hour.
If each storm follows their given pattern, which storm will become a hurricane first?
Answers
GPT-4o mini
To determine which storm will become a hurricane first, we need to identify when the wind speeds for both storms reach at least 74 miles per hour.
**For Tropical Storm Albert:**
The wind speed is given by the equation \( y = 2x + 55 \).
To find when this wind speed reaches 74 mph, we set the equation equal to 74:
\[
2x + 55 = 74
\]
Subtracting 55 from both sides:
\[
2x = 19
\]
Now, divide by 2:
\[
x = 9.5
\]
This means Tropical Storm Albert will become a hurricane after 9.5 hours.
**For Tropical Storm Betty:**
From the graph, we see that Tropical Storm Betty starts at a wind speed of 40 mph at time \( x = 0 \) and reaches 60 mph at time \( x = 5 \). To find the rate of change, we can determine the slope of the line:
The points (0, 40) and (5, 60) yield a slope of:
\[
\text{slope} = \frac{60 - 40}{5 - 0} = \frac{20}{5} = 4
\]
Thus, the wind speed function for Storm Betty can be expressed as:
\[
y = 4x + 40
\]
Now, we need to find when Storm Betty reaches 74 mph:
\[
4x + 40 = 74
\]
Subtracting 40 from both sides:
\[
4x = 34
\]
Dividing by 4 gives:
\[
x = 8.5
\]
This means Tropical Storm Betty will become a hurricane after 8.5 hours.
**Comparison of Times:**
- Tropical Storm Albert becomes a hurricane at 9.5 hours.
- Tropical Storm Betty becomes a hurricane at 8.5 hours.
**Conclusion:**
Tropical Storm Betty will become a hurricane first, at 8.5 hours after entering the Gulf of Mexico.
**For Tropical Storm Albert:**
The wind speed is given by the equation \( y = 2x + 55 \).
To find when this wind speed reaches 74 mph, we set the equation equal to 74:
\[
2x + 55 = 74
\]
Subtracting 55 from both sides:
\[
2x = 19
\]
Now, divide by 2:
\[
x = 9.5
\]
This means Tropical Storm Albert will become a hurricane after 9.5 hours.
**For Tropical Storm Betty:**
From the graph, we see that Tropical Storm Betty starts at a wind speed of 40 mph at time \( x = 0 \) and reaches 60 mph at time \( x = 5 \). To find the rate of change, we can determine the slope of the line:
The points (0, 40) and (5, 60) yield a slope of:
\[
\text{slope} = \frac{60 - 40}{5 - 0} = \frac{20}{5} = 4
\]
Thus, the wind speed function for Storm Betty can be expressed as:
\[
y = 4x + 40
\]
Now, we need to find when Storm Betty reaches 74 mph:
\[
4x + 40 = 74
\]
Subtracting 40 from both sides:
\[
4x = 34
\]
Dividing by 4 gives:
\[
x = 8.5
\]
This means Tropical Storm Betty will become a hurricane after 8.5 hours.
**Comparison of Times:**
- Tropical Storm Albert becomes a hurricane at 9.5 hours.
- Tropical Storm Betty becomes a hurricane at 8.5 hours.
**Conclusion:**
Tropical Storm Betty will become a hurricane first, at 8.5 hours after entering the Gulf of Mexico.