SOLUTION: Please help me solve this problem : Two plans travel at right angels to each other after leaving the same airport at the same time . One hour later they are 260 miles apart .If one

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Please help me solve this problem : Two plans travel at right angels to each other after leaving the same airport at the same time . One hour later they are 260 miles apart .If one      Log On


   

Question 1075691: Please help me solve this problem : Two plans travel at right angels to each other after leaving the same airport at the same time . One hour later they are 260 miles apart .If one travels 140 miles per
hour faster than the other .What is the rate of each ?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+=+1+ = time in hrs the planes have been flying
Let +r%5B1%5D+ = the rate in mi/hr of the slower plane
+r%5B1%5D+%2B+140+ = the rate in mi/hr of the faster plane
---------------------------
+%28+r%5B1%5D%2At+%29%5E2+%2B+%28+%28+r%5B1%5D+%2B+140+%29%2At+%29%5E2+=+260%5E2+
+%28+r%5B1%5D%2A1+%29%5E2+%2B+%28+%28+r%5B1%5D+%2B+140+%29%2A1+%29%5E2+=+260%5E2+
+r%5B1%5D%5E2+%2B+%28+r%5B1%5D+%2B+140+%29%5E2+=+260%5E2+
+r%5B1%5D%5E2+%2B+r%5B1%5D%5E2+%2B+280r%5B1%5D+%2B+19600+=+67600+
+2r%5B1%5D%5E2+%2B+280r%5B1%5D+-+48000+=+0+
+r%5B1%5D%5E2+%2B+140r%5B1%5D+-+24000+=+0+
+r%5B1%5D+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+140+
+c+=-24000+
-------------------
+r%5B1%5D+=+%28+-140+%2B-+sqrt%28+140%5E2-4%2A1%2A%28-24000%29+%29%29%2F%282%2A1%29+
+r%5B1%5D+=+%28+-140+%2B-+sqrt%28+19600+%2B+96000+%29%29+%2F+2+
+r%5B1%5D+=+%28+-140+%2B-+sqrt%28+115600+%29%29+%2F+2+
+r%5B1%5D+=+%28+-140+%2B+340+%29+%2F+2+
+r%5B1%5D+=+200%2F2+
+r%5B1%5D+=+100+
and
+r%5B1%5D+%2B+140+=+100+%2B+140+
+r%5B1%5D+%2B+140+=240+
Their rates are:
100 mi/hr and
240 mi/hr
------------------
check:
+%28+r%5B1%5D%2At+%29%5E2+%2B+%28+%28+r%5B1%5D+%2B+140+%29%2At+%29%5E2+=+260%5E2+
+%28+100%2A1+%29%5E2+%2B+%28+240%2A1+%29%5E2+=+260%5E2+
+10000+%2B+57600+=+67600+
+67600+=+67600+
OK