Flying against the wind, a jet travels 3040 miles in 4 hours.Flying with the wind, the same jet travels 8260 miles in 7 hours. What is the rate of the jet in still air, and what is the rate of the wind?

Foemicofeduz

Foemicofeduz

Answered question

2023-01-12

Flying against the wind, a jet travels 3040 miles in 4 hours. Flying with the wind, the same jet travels 8260 miles in 7 hours. What is the rate of the jet in still air, and what is the rate of the wind?

Answer & Explanation

Marvin Snyder

Marvin Snyder

Beginner2023-01-13Added 6 answers

Calculating the wind and jet speeds:
Step-1: Using an assumption, calculating the jet's speed both with and against the wind
Given that the jet travels 3040 miles in 4 hours against the wind. Thus, when compared to the wind, the jet's speed is 30404=760miles/hr.
Again, given that the jet travels 8260 miles in hours with the wind. Hence, the velocity of the jet with the wind is 82607=1180miles/hr.
Let the rate of the jet in still air be umiles/hr and the rate of wind be vmiles/hr.
Hence, the resultant rate of the jet against wind will be u-vmiles/hr and with the wind will be u+vmiles/hr.
Therefore, we must have:
u+v=11801
u-v=7602
Step-2: Finding uand v
Adding the equations 1 and 2, we get:
u+v+u-v=1180+7602u=1940u=19402u=970
Then,
v=1180-u=1180-970=210
Therefore, the rate of the jet in still wind is u=970miles/hr and the rate of the wind is v=210miles/hr.

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