Question 31725
1.
A total distance of 720 miles with x sppeed:
Equation:
*[tex \frac{720}{x-30}+\frac{720}{x+30)=10]
<pre><b><i>Cross multiply</i>
720[(x+30)+(x-30)]=10[(x+30)(x-30)]
{{{1440x=10(x^2-900)}}}
{{{10x^2-1440x-9000}}}
Divide the equation by 10:
*[tex x^2-144x-900=0]
Use the quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
a=1, b=-144, c=-900
{{{x = (-(-144) +- sqrt( (-144)^2-4*1*-900 ))/(2*1) }}}
{{{x=(144+-sqrt( 20736+3600))/2}}}
{{{x=(144+-sqrt(24336))/2}}} --->Remove the negative:
{{{x=(144+156)/2}}}
x=150
<font color = red>Hence, the speed of the plane is 150mph.</font>

2.{{{2/5=x-2/20}}}
Multiply the whole equation by 20 and simplfy:
{{{20(2/5)=20(x/1)-20(2/20)}}}
4(2)=20(x)-2
10=20x
x=0.5

3.Simple intest is given by A=(prinicpal * Time * rate)/100 
Let the rate be x:
*[tex 165=\frac{1500*1*x}{100}]
1500x=16500
x=11 (rate)
A={{{(2500*1*11)/100}}}
x=275
<font color = purple>Hence, the rate is 11% and with he same rate the money earned is $275.</font>
Paul.