Question 30097
<pre><b>Let the speed be x (orignal)
increased speed = x+100
30 minutes =0.5hours
Equation:
*[tex \frac{2800}{x+100}-\frac{2800}{x}=0.5]
{{{2800((x+100)-(x))=0.5((x)(x+100))}}}

{{{2800(100)=0.5(x^2+100x)}}}
{{{280000=0.5x^2+50x}}}
{{{0.5x^2+50x-280000=0}}}


{{{x=(-b+-sqrt(b^2-4*a*c))/(2*a)}}}
a=0.5, b=50, c=-280000
{{{x=(-50+-sqrt(50^2-4*0.5*-280000))/(2*0.5)}}}
Simplfy and you get two solutions:
x=-800 and x=700
Remove the negavtive
x=700
700+100=800


<font color = red>Hence, the speed of the new planes is 800km/h</font>
Paul.