Question

An airplane flying into a headwind travels the 1800-mile flying distance between Pittsburgh, Pennsylvania and Phoenix, Arizona in 3 hours and 36 minutes. On the return flight, the distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant. Select one: a. 550 miles per hour, 50 miles per hour b. 750 miles per hour, 25 miles per hour c. 1050 miles per hour, 50 miles per hour d. 500 miles per hour, 100 miles per hour

Answer 1

Answer:

50mph

Step-by-step explanation:

Against wind DATA:

distance = 1800 miles; time = (216/60) hrs ; rate = d/r = 500 mph

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With wind DATA:

distance = 1800 miles ; time = 3 hrs ; rate = d/r = 600 mph

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Equations:

p + w = 600

p - w = 500

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2p = 1100

p = 550 (speed of the plane in still air

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p + w = 600

w = 50 mph (speed of the wind current)

Answer 2

Answer: The correct option is a.

The air speed of the plane and the speed of the wind, assuming both remain constant are 550 miles per hour, 50 miles per hour respectively.

Step-by-step explanation:

Step 1: The given data

Distance flown by the plane for departure, d = 1800 miles

Distance flown by the plane while returning, d = 1800 miles

Time taken by the plane while departing, $t_1$ = 3 hours 36minutes = 3.6 h

Time taken by the plane while returning, $t_1$ = 3 hours = 3 h

Step 2: Find the speed of the flight during departure.

Let the speed of plane be v and that of head wind be v'

During headwind v' is acting against the direction of plane therefore net speed decreases, due to drag

Therefore,

$v-v'=\frac{d}{t_1}\\v-v'=\frac{1800}{3.6}\\v-v'=500 mph^{-1}------ > 1$

Step 3: Find the speed of the plane during the return.

The headwind v' is now acting with the direction of plane therefore net speed increases, due to push by wind

Therefore,

$v-v'=\frac{d}{t_2}\\v-v'=\frac{1800}{3}\\v-v'=600 mph^{-1}------ > 2$

Step 4: Find the speed of plane as well as headwind

For speed of plane add equation 1 and 2

$2v = 1100\\v = \frac{1100}{2}\\v = 550 mph{-1}$

For speed of headwind subtract equation 2 from 1

$2v' = 100\\v = \frac{100}{2}\\v = 50 mph{-1}$

Therefore, The air speed of the plane and the speed of the wind, assuming both remain constant are 550 miles per hour, 50 miles per hour respectively.

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