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

Answer:

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

Step-by-step 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

$t_1 = \dfrac{1000miles}{600mph}$

$\boxed{ t_1 = 1.67hr}$

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

$t_2 = \dfrac{1000miles}{400mph}$

$\boxed{t_2 = 2.5hr. }$

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