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An airplane cruises at 880km/h relative to the air. It is flying from Denver, Colorado, due west to Reno, Nevada, a distance of 1200km, and will then return. There is a steady 90km/h wind blowing to the east. What is the difference in flight time between the two legs?

Answer :

MichaelLiu
This should go in mathematics, but I'll answer anyway.
When the airplane goes west, then the wind will be pushing back on it, so the speed of the plane will go down to 790 km/h. 1200/790 is how long it will take for it to get to Reno. When it comes back, it gets a speed boost from the wind. Its new speed will be 880+90=970 1200/970 is how long it will take for the plane to return. 1200/790 - 1200/970 is your answer. 1.52-1.24=0.28
0.28 hours

Answer:

[tex]\Delta t = 0.28 hours[/tex]

Explanation:

While airplane is flying from Denver to Colorado

then the speed of plane is opposite to that wind speed

so here time to reach the destination is given as

[tex]t = \frac{d}{v}[/tex]

[tex]t_1 = \frac{1200}{880 - 90}[/tex]

[tex]t_1 = 1.52 h[/tex]

Now while its return Journey we know that air is flowing in the same direction as that of airplane motion

so we will have

[tex]t_2 = \frac{1200}{880 + 90}[/tex]

[tex]t_2 = 1.24 hr[/tex]

So total time leg in two travels is given as

[tex]\Delta t = t_1 - t_2[/tex]

[tex]\Delta t = 1.52 - 1.24[/tex]

[tex]\Delta t = 0.28 hours[/tex]

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