Final answer:
The speed of the jet stream is calculated to be 210 miles per hour by setting up an equation using the distances flown and time, with the given plane airspeed of 700 mph, and solving for the speed of the jet stream.
Step-by-step explanation:
To solve the problem where a plane can fly 1300 miles east with the jet stream in the same amount of time it takes to fly 700 miles west against the jet stream, and knowing that the plane has an airspeed of 700 miles per hour, we have to set up two equations that represent the time it takes for each trip. Since time equals distance divided by speed, and we know the times are equal, we can write:
- Time east with the jet stream = 1300 miles / (700 mph + jet stream speed)
- Time west against the jet stream = 700 miles / (700 mph - jet stream speed)
Since the times are equal, we can set the two expressions equal to each other:
1300 / (700 + j) = 700 / (700 - j)
Here, 'j' represents the speed of the jet stream. Solving for 'j', we multiply both sides of the equation by the denominators to clear the fractions:
1300 × (700 - j) = 700 × (700 + j)
This leads to:
910000 - 1300j = 490000 + 700j
Now we combine like terms:
910000 - 490000 = 1300j + 700j
420000 = 2000j
And finally, divide both sides by 2000 to find the jet stream's speed:
j = 420000 / 2000
j = 210 mph
Therefore, the speed of the jet stream is 210 miles per hour.