A rocket is fired from Spain at a constant rate of 5 meters per second toward France. After the rocket had traveled 10 meters, France launches a rocket right behind it to catch it at a rate of 6.5 meters per sec. When will the France rocket intercept the Spain rocket, and how far wil they have traveled at the time of interception?
y=5x and y=6.5x + -13.
5x=6.5x + -13
x=8.66 and y=43. (Answer)
I don't understand where the -13 comes from in setting up the problem. I understand the rest. Please help.
You know speed of rocket launcged from spain its $5m/s$ it has travelled 10m which implies time is $2$ seconds so the gap between time is $2$ seconds . We know $d=s.t$ so the distance gap will be $6.5*2=13$. Now lets answer your question if you know the concept of relative velocity then its clear. If both rockets travel in same direction then its $-13$ if in opposite direction then $+13$.