Question 830206
j time jogging
w time walking


_________________speed_________________time_______________distance
jogging__________7.5___________________j__________________(____)
walking__________4_____________________w__________________(____)
Total_________________________________3_____________________15



{{{highlight_green(R*t=d)}}} for Rate, time, distance.


_________________speed_________________time_______________distance
jogging__________7.5___________________j__________________((7.5)j)
walking__________4_____________________w__________________(4w)
Total_________________________________3_____________________15


{{{highlight(j+w=3)}}} and {{{highlight((7.5)j+4w=15)}}}
You have the correct equations.  That is more than half of the solution process.
You are worried about some "right" method to solve the system of equations.  Take your choice:  Substitution, Elimination, or Matrix.


Let me assume that you had only a temporary difficulty and that you should try solving the system again and find no trouble.


....
As for what I'd do, my choice is Elimination Method.  Multiply the time equation by 4; subtract this equation from the distance equation, and you will have an equation in only the variable, j, and can quickly get the value for j.