Question

On a recent flight from Phoenix to Kansas City, a distance of 919 nautical miles, the plane arrived 20 minutes early. On leaving the aircraft, a passenger asked the captain, "what was our tail wind?" He replied, "I don't know, but our ground speed was 550 knots." Is there enough information provided to find the tail wind? If possible, find the tail wind. [1 knot= 1 nautical mile]

Answer 1

Let airspeed and tailwind equal the airspeed and the tailwind speed respectively.
r t = d
The flight time with the tailwind was distance divided by ground speed, 919/515 hours.
Without the tailwind the flight takes 20 minutes longer.

Solve the following equations for airspeed and tailwind:\[\left\{(\text{airspeed}+\text{tailwind})\frac{919}{550}=919,\text{airspeed}\left(\frac{919}{550}+\frac{20}{60}\right)=919\right\}\]\[\left\{\text{airspeed}=\frac{1516350}{3307},\text{tailwind}=\frac{302500}{3307}\right\} \]\[\{\text{airspeed}=458.5 \text{mph},\text{tailwind}=91.5 \text{mph}\} \]

Answer 2

that's awesome thank you for the thorough response, helps a lot! =)

Answer 3

Your welcome.

Answer 4

quick question, how did you get 302500 and 1516350 for the numerators?

Answer 5

I used Mathematica to do the "clerical work". To get an exact number only whole fractions should be used. Mathematica presents fractions in a reduced form, so if one were to manually solve the equations using pencil and paper, then the fractions obtained may appear to be different.

Also Mathematica is capable of unlimited precision with integers. It can deal with integers far larger than a hand calculator can manage. For example here is 160! (160 factorial)

471472363599206132240694321176194377951192623045460204976904578317542573467421580346978030238114995699562728104819596262106947389303901748942909887857509625114880781313585012959529941660203611234871833992565791817698209861793313332044734813700096000000000000000000000000000000000000000

Answer 6

=) thanks