document.write( "Question 74969: Please can somebody help me in this problem:
\n" ); document.write( "It took a small plane 2 hours to fly 375 miles against the
\n" ); document.write( "wind than it took the same plane to fly the same distance
\n" ); document.write( "with the wind. The rate of the wind was 25 mph. Find the
\n" ); document.write( "rate of the plane in caalm air. \n" ); document.write( "
Algebra.Com's Answer #53894 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
It took a small plane 2 hours to fly 375 miles against the
\n" ); document.write( "wind than it took the same plane to fly the same distance
\n" ); document.write( "with the wind. The rate of the wind was 25 mph. Find the
\n" ); document.write( "rate of the plane in calm air.
\n" ); document.write( ":
\n" ); document.write( "Let s = speed of the plane in calm air
\n" ); document.write( "Then:
\n" ); document.write( "(s+25) = speed with the wind
\n" ); document.write( "and
\n" ); document.write( "(s-25) = speed against the wind
\n" ); document.write( ":
\n" ); document.write( "Write a time equation, Time = distance/speed; (distance given as 375 mi)
\n" ); document.write( ":
\n" ); document.write( "Time with the wind + 2hr = Time against the wind
\n" ); document.write( "\"375%2F%28%28s%2B25%29%29\" + 2 = \"375%2F%28%28s-25%29%29\"
\n" ); document.write( ":
\n" ); document.write( "Multiply equation by the common denominator, (s+25)(s-25); resulting in:
\n" ); document.write( "375(s-25) + 2(s+25)(s-25) = 375(s+25)
\n" ); document.write( ":
\n" ); document.write( "Multiply what's inside the brackets:
\n" ); document.write( "375s - 9375 + 2(s^2 - 625) = 375s + 9375
\n" ); document.write( ":
\n" ); document.write( "375s - 9375 + 2s^2 - 1250 = 375s + 9375
\n" ); document.write( ":
\n" ); document.write( "Group like terms on the left:
\n" ); document.write( "2s^2 + 375s - 375s - 9375 - 1250 - 9375 = 0
\n" ); document.write( ":
\n" ); document.write( "2s^2 - 20000 = 0
\n" ); document.write( ":
\n" ); document.write( "Add 20000 to both sides:
\n" ); document.write( "2s^2 = +20000
\n" ); document.write( ":
\n" ); document.write( "s^2 = 20000/2
\n" ); document.write( ":
\n" ); document.write( "s^2 = 10000
\n" ); document.write( ":
\n" ); document.write( "s = \"sqrt%2810000%29\"
\n" ); document.write( ":
\n" ); document.write( "s = 100 mph in calm air
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check our solution by finding the time at both speeds:
\n" ); document.write( "With the wind = 125 mph, and against = 75 mph
\n" ); document.write( "375/75 = 5 hrs
\n" ); document.write( "375/125= 3 hrs
\n" ); document.write( "---------------
\n" ); document.write( "Differ = 2 hrs
\n" ); document.write( ":
\n" ); document.write( "How about this, did it make sense to you? Any questions?\r
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