A plane traveled 5525 miles with the wind in 8.5 hours and 4505 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind. The speed of the plane in still air is (Hours, Miles, Mph) Simplify your answer.

The speed of the plane in still air is 590Mph

The speed of the wind is 60Mph

Step-by-step explanation:

Let

s= the speed of the plane in still air

w= the speed of the wind

Flying with the wind:

5525=(s+w)*8.5

5525=8.5s + 8.5w (1)

Flying against the wind:

4505=(s-w)*8.5

4505=8.5s - 8.5w (2)

Add (1) and (2) to eliminate w

5525=8.5s + 8.5w

4505=8.5s - 8.5w

10,030=17s

Divide both sides by 17

10,030/17=17s/17

590=s

s=590Mph

Substitute the value of s into (1)

5525=8.5s + 8.5w

5525=8.5(590) + 8.5w

5525=5,015 + 8.5w

5525-5015=8.5w

510=8.5w

Divide both sides by 8.5

60=w

w=60Mph

The speed of the plane in still air is 590Mph

The speed of the wind is 60Mph

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step-by-step explanation:

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