SOLUTION: the speed of wind is 6 mph. a hummingbird flies for 24 minutes with the wind to a food source. it takes 36 minutes to return (into the wind) from the food source. find the speed of

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: the speed of wind is 6 mph. a hummingbird flies for 24 minutes with the wind to a food source. it takes 36 minutes to return (into the wind) from the food source. find the speed of      Log On

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Question 995952: the speed of wind is 6 mph. a hummingbird flies for 24 minutes with the wind to a food source. it takes 36 minutes to return (into the wind) from the food source. find the speed of the hummingbird in still air
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Convert minutes to hours:
+24%2F60+=+.4+ hrs
+36%2F60+=+.6+ hrs
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Let +s+ = the speed of the hummingbird in still air
+s+%2B+6+ = bird's speed flying with the wind
+s+-+6+ = bird's speed flying against the wind
Let +d+ = the one-way distance the bird flies
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Equation for flying with the wind:
(1) +d+=+%28+s%2B6+%29%2A.4+
Equation for flying against the wind:
(2) +d+=+%28+s-6+%29%2A.6+
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Substitute (1) into (2)
+%28+s%2B6+%29%2A.4+=+%28+s-6+%29%2A.6+
+.4s+%2B+2.4+=+.6s+-+3.6+
+.2s+=+6+
+s+=+30+
The speed of the hummingbird in still air is 30 mi/hr
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check:
(1) +d+=+%28+s%2B6+%29%2A.4+
(1) +d+=+%2830%2B6+%29%2A.4+
(1) +d+=+36%2A.4+
(1) +d+=+14.4+
and
(2) +d+=+%28+s-6+%29%2A.6+
(2) +d+=+%28+30-6+%29%2A.6+
(2) +d+=+24%2A.6+
(2) +d+=+14.4+
OK