document.write( "Question 741083: A search plane takes off from an airport at 6:00 a.m. and travels north at 200mph. A second plane leaves that airport at 6:30 a.m. and travels east at 150mph. The planes carry radios with a maxium range of 300 miles. When (to the nearest minute) will these planes no longer be able to communicate? \n" ); document.write( "

Algebra.Com's Answer #451838 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The 1st plane has a head start of
\n" ); document.write( " $\"+d%5B1%5D+=+200%2A%281%2F2%29+\"$
\n" ); document.write( " $\"+d%5B1%5D+=+100+\"$ mi
\n" ); document.write( "----------------
\n" ); document.write( "Start a stopwatch when the 2nd plane leaves
\n" ); document.write( "------------------------------
\n" ); document.write( "Let $\"+t+\"$ = time on stopwatch when they
\n" ); document.write( "are $\"+300+\"$ miles apart
\n" ); document.write( "---------------------
\n" ); document.write( "distance for 1st plane:
\n" ); document.write( " $\"+100+%2B+200t+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "Distance for 2nd plane:
\n" ); document.write( " $\"+150t+\"$
\n" ); document.write( "-------------
\n" ); document.write( "The planes travel 90 degrees to each other, so
\n" ); document.write( " $\"+%28+100+%2B+200t+%29%5E2+%2B+%28150t%29%5E2+=+300%5E2+\"$
\n" ); document.write( " $\"+100%5E2%2A%28+1+%2B+2t+%29%5E2+%2B+22500t%5E2+=+90000+\"$
\n" ); document.write( " $\"+10000%2A%28+1+%2B+4t+%2B+4t%5E2%29+%2B+22500t%5E2+=+90000+\"$
\n" ); document.write( " $\"+10000+%2B+40000t+%2B+40000t%5E2+%2B+22500t%5E2+=+90000+\"$
\n" ); document.write( " $\"+62500t%5E2+%2B+40000t+-+80000+=+0+\"$
\n" ); document.write( " $\"+625t%5E2+%2B+400t+-+800+=+0+\"$
\n" ); document.write( " $\"+25t%5E2+%2B+16t+-+32+\"$
\n" ); document.write( "Use quadratic formula
\n" ); document.write( " $\"+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+25+\"$
\n" ); document.write( " $\"+b+=+16+\"$
\n" ); document.write( " $\"+c+=+-32+\"$
\n" ); document.write( " $\"+t+=+%28-16+%2B-+sqrt%28+16%5E2+-+4%2A25%2A%28-32%29+%29%29+%2F+%282%2A25%29+\"$
\n" ); document.write( " $\"+t+=+%28-16+%2B-+sqrt%28+256+%2B+3200+%29%29+%2F+50+\"$
\n" ); document.write( " $\"+t+=+%28-16+%2B-+sqrt%28+3456+%29%29+%2F+50+\"$
\n" ); document.write( " $\"+t+=+%28+-16+%2B+58.788+%29+%2F+50+\"$
\n" ); document.write( " $\"+t+=+42.788+%2F+50+\"$
\n" ); document.write( " $\"+t+=+.856+\"$ hrs
\n" ); document.write( " $\"+6.5+%2B+.856+=+7.356+\"$
\n" ); document.write( " $\"+.356%2A60+=+22+\"$ min
\n" ); document.write( "They will be out of range at 7:22
\n" ); document.write( "check:
\n" ); document.write( "1st plane:
\n" ); document.write( " $\"+d+=+100+%2B+200%2A.856+\"$
\n" ); document.write( " $\"+d+=+100+%2B+171.2+\"$
\n" ); document.write( " $\"+d+=+271.2+\"$
\n" ); document.write( "--------------
\n" ); document.write( "2nd plane:
\n" ); document.write( " $\"+d+=+150%2A.856+\"$
\n" ); document.write( " $\"+d+=+128.4+\"$
\n" ); document.write( "-------------
\n" ); document.write( " $\"+271.2%5E2+%2B+128.4%5E2+=+300%5E2+\"$
\n" ); document.write( " $\"+73549.4+%2B+16486.6+=+90000+\"$
\n" ); document.write( " $\"+90036+=+90000+\"$
\n" ); document.write( "Maybe error is due to rounding off.
\n" ); document.write( "Recheck my math- I think the method
\n" ); document.write( "is OK \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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