Respuesta :
Answer:
The jet stream speed used by the computer is 142.[tex]\overline {857142}[/tex] km/h
Explanation:
The given parameters are;
The distance between the two cities the plane flies = 4,000 km
The difference in flight times for outgoing and return flights = 70.0 min
We note that 70 min = 70 min × 1 h/60 min = 7/6 h
The airspeed recommended by the airline computer = 1,000 km/h
Let 'a' represent the jet stream speed
The time it takes the plane moving in the same direction as the jet stream between the two cities, 't₁', is given as follows;
[tex]t_1 = \dfrac{4000}{1000 + a}[/tex]
The time it takes the plane moving in the opposite direction as the jet stream between the two cities, 't₂', is given as follows;
[tex]t_2 = \dfrac{4000}{1000 - a}[/tex]
The difference in flight times for outgoing and return flights, Δt = t₂ - t₁
Therefore, we have;
[tex]\Delta t = t_2 - t_1 = \dfrac{4000}{1000 - a} - \dfrac{4000}{1000 + a} = \dfrac{7}{6}[/tex]
From which we get;
[tex]-\dfrac{8000 \cdot a}{a^2 -1,000,000} = \dfrac{7}{6}[/tex]
By cross multiplying, we have;
-48,000·a = 7·a²- 7,000,000
∴ 7·a² + 48,000·a - 7,000,000 = 0
Factorizing with a graphic calculator gives;
(7·a - 1,000)·(a + 7,000) = 0
∴ a = 1,000/7, or a = -7000
Therefore, the jet stream speed the computer is using, a = 1,000/7 km/h = 142.[tex]\overline {857142}[/tex] km/h.
