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
