Question

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?

Answer 1

Answer:

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