Question 1124025
Plane {{{B}}} is flying {{{55mph}}} faster than Plane {{{A}}}. 
if plane {{{B}}}  is flying {{{v=xmph}}}, then plane {{{A}}} is flying {{{v=(x-55)mph}}}
for time {{{t}}}


Find the time it takes for Plane {{{A }}}to travel {{{1800}}} miles if it takes Plane {{{B}}} the same amount of time to travel {{{1965}}} miles.

distance formula: {{{d=v*t}}} 
=>{{{t=d/v}}} 

for Plane A to travel {{{d=1800mil}}} will take

{{{t=1800/(x-55)}}}  ....eq.1

 if it takes Plane B the same amount of time to travel {{{1965mil}}}, we have

{{{t=1965/x}}} ......eq.2

from eq.1 and eq.2:

{{{1800/(x-55)=1965/x}}} 
{{{1800x=1965(x-55)}}} 
{{{1800x=1965x-108075}}} 
{{{108075=1965x-1800x  }}} 
{{{108075=165x }}} 
{{{x=655mph }}} 

so, 
{{{x=655mph}}} -> rate of Plane {{{B}}}
then
{{{x-55=600mph}}} -> rate of Plane {{{A}}}


for Plane A to travel {{{d=1800mil}}} will take
{{{d=v*t}}} 
{{{1800mil=600(mil/h)*t}}} 
{{{t=1800mil/600(mil/h)}}} 
{{{t=3h}}} ->the time it takes for Plane {{{A }}}to travel {{{1800}}} miles

check time for plane {{{B}}}:

{{{1965mil=655(mil/h)*t}}} 
{{{t=1965mil/655(mil/h)}}} 
{{{t=3h}}} -> so, proves that the time is same