A plane flies from NY to Chicago, which is about 700 miles, at a speed of 330 mph. How long does the flight take? On a return trip, a tailwind (x) helps the plane move faster. (The plane still operates to produce a basic speed of 330 mph. The total flying time for the round trip is 3.7 hours so how fast is the tailwind?

Flight takes 2.12 hrs from NY to chicago

The tailwind speed was x = 143.4 mph

Step-by-step explanation:

Given:-

- The distance from NY to Chicago, d = 700 miles

- The speed of plane, vo = 330 mph

- The speed of tailwind = x

- The total time for round trip T = 3.7 hrs

Find:-

How long does the flight take?

how fast is the tailwind?

Solution:-

- The total time "T" of the round-trip consists of time taken "t1" for journey from NY to Chicago and time taken "t2" from Chicago to NY.

- Time taken from NY to Chicago (t1) = d / vo

                                                           = 700 / 330

                                                           = 2.1212 hrs

- Whereas, the time time taken (t2) on return journey from Chicago to NY with the help of tailwind with speed x was:

- Time taken from Chicago to NY (t2) = d / (vo+x)

- The total time taken for round-trip = T

- We will sum individual times "t1" and "t2" and equate to "T"

                     2.1212 + 700 / ( 300 + x ) = 3.7

- Re-arrange and solve for x:

                      700 = (3.7 - 2.1212)*(300 + x )

                      700 = 473.6364 + 1.5788x

                      x = 226.3636/1.5788

                      x = 143.38 mph

she will travel a distance in the range of 3 - 11 miles