SOLUTION: 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 radi

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: 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 radi      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The 1st plane has a head start of
+d%5B1%5D+=+200%2A%281%2F2%29+
+d%5B1%5D+=+100+ mi
----------------
Start a stopwatch when the 2nd plane leaves
------------------------------
Let +t+ = time on stopwatch when they
are +300+ miles apart
---------------------
distance for 1st plane:
+100+%2B+200t+
-------------------
Distance for 2nd plane:
+150t+
-------------
The planes travel 90 degrees to each other, so
+%28+100+%2B+200t+%29%5E2+%2B+%28150t%29%5E2+=+300%5E2+
+100%5E2%2A%28+1+%2B+2t+%29%5E2+%2B+22500t%5E2+=+90000+
+10000%2A%28+1+%2B+4t+%2B+4t%5E2%29+%2B+22500t%5E2+=+90000+
+10000+%2B+40000t+%2B+40000t%5E2+%2B+22500t%5E2+=+90000+
+62500t%5E2+%2B+40000t+-+80000+=+0+
+625t%5E2+%2B+400t+-+800+=+0+
+25t%5E2+%2B+16t+-+32+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+25+
+b+=+16+
+c+=+-32+
+t+=+%28-16+%2B-+sqrt%28+16%5E2+-+4%2A25%2A%28-32%29+%29%29+%2F+%282%2A25%29+
+t+=+%28-16+%2B-+sqrt%28+256+%2B+3200+%29%29+%2F+50+
+t+=+%28-16+%2B-+sqrt%28+3456+%29%29+%2F+50+
+t+=+%28+-16+%2B+58.788+%29+%2F+50+
+t+=+42.788+%2F+50+
+t+=+.856+ hrs
+6.5+%2B+.856+=+7.356+
+.356%2A60+=+22+ min
They will be out of range at 7:22
check:
1st plane:
+d+=+100+%2B+200%2A.856+
+d+=+100+%2B+171.2+
+d+=+271.2+
--------------
2nd plane:
+d+=+150%2A.856+
+d+=+128.4+
-------------
+271.2%5E2+%2B+128.4%5E2+=+300%5E2+
+73549.4+%2B+16486.6+=+90000+
+90036+=+90000+
Maybe error is due to rounding off.
Recheck my math- I think the method
is OK