To solve the problem, we need to determine the speed of the jet in still air and the speed of the wind. We'll denote:
- \( j \) as the speed of the jet in still air (in miles per hour).
- \( w \) as the speed of the wind (in miles per hour).
According to the information given:
- The jet travels 4410 miles against the wind in 6 hours.
- The jet travels 5610 miles with the wind in the same amount of time.
From this information, we can set up two equations based on the formula distance = speed × time.
For the trip against the wind:
The effective speed against the wind is \( j - w \). The equation for this trip is:
\[ j - w = \frac{4410 \text{ miles}}{6 \text{ hours}} = 735 \text{ mph} \]
For the trip with the wind:
The effective speed with the wind is \( j + w \). The equation for this trip is:
\[ j + w = \frac{5610 \text{ miles}}{6 \text{ hours}} = 935 \text{ mph} \]
Now, we have a system of equations:
- \( j - w = 735 \)
- \( j + w = 935 \)
To solve for \( j \) and \( w \):
We can add the two equations together:
\[ (j - w) + (j + w) = 735 + 935 \] \[ 2j = 1670 \] \[ j = \frac{1670}{2} = 835 \text{ mph} \]
Next, we substitute \( j \) back into one of the original equations to find \( w \). We can use the first equation:
\[ 835 - w = 735 \] \[ w = 835 - 735 = 100 \text{ mph} \]
Conclusion:
The speed of the jet in still air is 835 mph, and the speed of the wind is 100 mph.
Regarding your question about "what is the date of the jet still in air," it seems there may have been a misunderstanding or a miscontext. Could you please clarify what you meant by that?
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