document.write( "Question 67071This question is from textbook Algebra 1
\n" ); document.write( ": Against a head wind, Jeff computes his flight time for a trip of 2900 miles at 5 hours. The flight would take 4 hours and 50 minutes if the head wind were half as much. Find the head wind and the plane's air speed.
\n" ); document.write( "THANK YOU!!! \n" ); document.write( "
Algebra.Com's Answer #47750 by ankor@dixie-net.com(22740)\"\" \"About 
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Against a head wind, Jeff computes his flight time for a trip of 2900 miles at 5 hours. The flight would take 4 hours and 50 minutes if the head wind were half as much. Find the head wind and the plane's air speed.
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\n" ); document.write( "You must mean find the plane's speed in still air speed.
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\n" ); document.write( "Change 50 min to hrs: 50/60 = 5/6 hr; + 4 hr = 29/6 hrs
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\n" ); document.write( "Let s = the planes still air speed
\n" ); document.write( "Let w = wind speed.
\n" ); document.write( ":
\n" ); document.write( "Write two equations using the distance: dist = time * speed
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\n" ); document.write( "The 1st equation:
\n" ); document.write( "5(s - w) = 2900
\n" ); document.write( "Simplify divide equation by 5
\n" ); document.write( "s - w = 580
\n" ); document.write( "s = (w + 580)
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\n" ); document.write( "The 2nd equation, (wind is half as much)
\n" ); document.write( "(29/6)(s - .5w) = 2900
\n" ); document.write( "Get rid of this annoying fraction, mult eq by 6 and you have:
\n" ); document.write( "29(s-.5w) = 2900 * 6
\n" ); document.write( "29s - 14.5w = 17400\r
\n" ); document.write( "\n" ); document.write( ":
\n" ); document.write( "Substitute (w+580) for s in the 2nd equation, solve for w:
\n" ); document.write( "29(w+580) - 14.5w = 17400
\n" ); document.write( "29w + 16820 - 14.5w = 17400
\n" ); document.write( "29w -14.5w = 17400 - 16820
\n" ); document.write( "14.5w = 580
\n" ); document.write( "w = 580/14.5
\n" ); document.write( "w = 40 mph speed of the wind\r
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\n" ); document.write( "Find the speed of the plane
\n" ); document.write( "s = w + 580
\n" ); document.write( "s = 40 + 580
\n" ); document.write( "s = 620 mph is the speed of the plane
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\n" ); document.write( "Check our solution:
\n" ); document.write( "Wind speed 40 mph: 2900/580 = 5 hrs
\n" ); document.write( "Wind speed 20 mph: 2900/600 = 4.8333 hrs (which is 4 & 5/6 hrs) \r
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