Question 930541
A jet plane travelling at J mph over takes a propeller plane travelling at P mph that had a k hour head start.how far the starting point are the planes?



J=500, P=200, k=2.
Let d be the distance each travels by the time both went the same distance (and meet);
Let t be the time that the faster plane (jet) traveled until caught up to the slower plane.



__________________rate________time_________distance
JET_______________J____________t____________d
PROP______________P___________t+k___________d


Two variables, but the variable to solve for is d.  First you can solve for t if you want.  Maybe not the only way.


{{{system(Jt=d,P(t+k)=d)}}}



Solve for t in terms of d, no matter which equation you start with.
{{{t=d/J}}};
;
{{{P(t+k)=d}}}
{{{P(d/J+k)=d}}}
{{{Pd/J+Pk=d}}}
{{{Pd/J-d=-Pk}}}
{{{d(P/J-1)=-Pk}}}
{{{highlight(d=(-Pk)/(P/J-1))}}}
which you could simplify further...
{{{d=(-PkJ)/(P-J)}}}
in which you may check that P-J is a negative value...
{{{d=((-PJk)/(P-J))((-1)/(-1))}}}
{{{highlight(d=(PJk)/(J-P))}}}



Evaluate d for the specific exercise using the given values.