Question 162056
A plane carries enough fuel for 10 hours of flight at an airspeed of 150 miles per hour. How far can it fly into a 30 mph headwind and still have enough fuel to return to its starting point? (This distance is called the point of no return.)
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This assumes that the return will be going with the wind
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Let d = distance into the wind
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Speed against the wind: 150 - 30 = 120 mph
Speed with the wind: 150 + 30 = 180 mph
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Write a time equation: Time = {{{dist/speed}}}
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Time into the wind + time with the wind = 10 hrs
{{{d/120}}} + {{{d/180}}} = 10
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Multiply equation by 360 to get rid of the denominators:
360*{{{d/120}}} + 360*{{{d/180}}} = 360(10)
Cancel denominators
3d + 2d = 3600
d = {{{3600/5}}}
d = 720 mi to the point of no return
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Check solution by find the times
720/120 = 6 hr
720/180 = 4 hr
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endurance 10 hrs