An airplane is flying a round trip from NYC to San Fran (2,500 miles 1-way). The round-trip flight time is 10 hrs 25 mins. If the speed of the wind during the t

Question

A passenger airliner is flying a round trip from New York City to San
Francisco (2,500 miles 1-way). The round-trip flight time is 10 hours
and 25 mins. (Does not count the layover time). Given that the speed
of the wind during the round-trip is constant, calculate the speed of
the wind if the speed of the aircraft is 500 mph.

Answer 1

Let's call the speed of the wind x. Remember that distance = (rate)(time). We'll write one equation for the airplane's journey with the wind, and one for the airplane's journey against the wind.

 

 

 

WITH THE WIND:

 

The distance is 2,500 miles. The rate is the airplane's speed plus the speed of the wind, or 500 + x. We're not given the time, so call it t.

 

2500 = (500 + x)t

 

 

AGAINST THE WIND:

 

The distance is again 2,500 miles. The rate is the airplane's speed minus the speed of the wind, or 500 - x. We're not given the time, but we do know that its time plus t must be 10 hours and 25 minutes. In hours, that's 10 and 25/60 hours, which is 10 and 5/12 hours, which is 125/12 hours. So, the time is 125/12 - t.

 

2500 = (500 - x)(125/12 - t)

 

 

 

Now you have a system of two equations:

 

2500 = (500 + x)t

2500 = (500 - x)(125/12 - t)

 

Solve the first equation for t, then substitute that into the second equation and solve for x:

 

2500/(500 + x) = t

 

2500 = (500 - x)(125/12 - t)

2500 = (500 - x)(125/12 - 2500/(500 + x))

2500 = (500 - x)((125(500+x))/(12(500+x)) - (2500(12))/(12(500+x))

2500 = (500 - x)((125(500+x) - 2500(12))/(12(500+x))

2500(12)(500+x) = (500 - x)(125(500+x) - 2500(12))

30000(500+x) = (500 - x)(62500 + 125x - 30000)

15000000 + 30000x = (500 - x)(32500 + 125x)

15000000 + 30000x = 16250000 + 62500x - 32500x - 125x²

-1250000 + 30000x = 30000x - 125x²

-1250000 = -125x²

10000 = x²

±100 = x

 

Since speed is positive, ignore -100. The wind speed is a constant x = 100 mph.