Question

On a no wind day, an airplane is flying 2000 miles round trip from Chicago to Boston and back to Chicago with a constant speed of 500 mph. About how long would it take to fly the same round trip if there is a wind speed of 100 mph from Chicago to Boston during the whole round trip flight?

Answer 1

It would take the plane about 4.17 hours to fly the whole round trip.

Explanation:

Assuming that the distance from Chicago to Boston is 2000/2 = 1000 miles.

Since the wind is blowing from Chicago to Boston, when the plane is traveling to Boston, the velocity of the wind adds to the its velocity:

`v_1 = 500mph + 100mph = 600mph`;

therefore, the time it takes for the plane to go from Chicago to Boston is

`t_1 = (1000miles)/(600mph)`

`\boxed{ t_1 = 1.67hr}`

Now, as the plane flies back from Boston to Chicago, the wind is blowing opposite the direction of its movement; therefore, the wind's velocity subtracts from the velocity of the plane:

`v_2 = 500mph-100mph =400mph`

and the time taken during the trip is

`t_2 = (1000miles)/(400mph)`

`\boxed{t_2 = 2.5hr. }`

Therefore, the total time taken
`t_(tot)` during the whole round trip is

`t_(tot)= t_1+t_2 \\\\t_(tot) = 1.67hr+2.5hr \\`

`\boxed{t_(tot) = 4.17hr}`

Therefore, on the windy day, it would take the plane 4.17 hours to fly the whole round trip