Question

An airplane cruises at 900 km/h relative to the air. It is flying from Denver, Colorado, due west to Reno, Nevada, a distance of 1200 km, and will then return. There is a steady 80 km/h wind blowing to the east.

What is the difference in flight time between the two legs of the trip?

Answer 1

Speed of the plane with respect to the ground when moving towards west is,

$$ \begin{aligned} v_{P G} &=v_{P A}-v_{A G} \\ &=(900 \mathrm{~km} / \mathrm{h})-(80 \mathrm{~km} / \mathrm{h}) \\ &=(820 \mathrm{~km} / \mathrm{h}) \end{aligned} $$

Distance between two cities is \(1200 \mathrm{~km}\).

So, time taken for up journey is, \(\begin{aligned} t_{1} &=\frac{d}{v_{P G}} \\ &=\frac{1200 \mathrm{~km}}{820 \mathrm{~km} / \mathrm{h}} \\ &=1.46 \mathrm{~h} \end{aligned}\)

Speed of the plane with respect to the ground when moving towards east is,

$$ \begin{aligned} v_{P G} &=v_{P A}+v_{A G} \\ &=(900 \mathrm{~km} / \mathrm{h})+(80 \mathrm{~km} / \mathrm{h}) \\ &=(980 \mathrm{~km} / \mathrm{h}) \end{aligned} $$

So, time taken for retum journey is, \(t_{2}=\frac{1200 \mathrm{~km}}{980 \mathrm{~km} / \mathrm{h}}\)

\(=1.22 \mathrm{~h}\)

So, time difference between two journeys is,

$$ \begin{aligned} t &=t_{1}-t_{2} \\ &=(1.46 \mathrm{~h})-(1.22 \mathrm{~h}) \\ &=(0.23 \mathrm{~h})\left(\frac{60 \mathrm{~min}}{1 \mathrm{~h}}\right) \end{aligned} $$

\(=14.1 \mathrm{~min}\)