A man flies a small airplane from Fargo to Bismarck, North Dakota—a distance of

Algebra
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A man flies a small airplane from Fargo to Bismarck, North Dakota—a distance of 180 mi. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 h 15 min. What is his speed in still air, and how fast is the wind blowing?
speed in still air     mph
wind speed     mph
Apr 20th, 2015

Let  speed of plane x miles/hr and speed of still air = y miles/hr

speed = distance/time    ; 

while travelling along the wind time required = 1 hr 15 minutes    or 1.25 hrs

while traveling along the wind  (x+y) = 180/1.25      or x+y = 144 -------------(1)

while travelling against wind     x-y = 180/2      or     x-y = 90        -------------(2)

Adding Eq 1 & 2 we get

2x  =234  hence x = 117 miles/hr

therefore y = 27 miles/hr

Answer

speed in still air :  117 mph

wind speed     :     27 mph

Apr 20th, 2015

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