велик скорость x, пеший x-15. t время велика, пеший t+3.
Формула S = x*t, S - расстояние равное 100км.
![\left \{ {{x*t=100} \atop {(x-15)(t+3)=100}} \right. \left \{ {{x*t=100} \atop {(x-15)(t+3)=100}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx%2At%3D100%7D%20%5Catop%20%7B%28x-15%29%28t%2B3%29%3D100%7D%7D%20%5Cright.)
![\left \{ {{x=\frac{100}{t}} \atop {(x-15)(t+3)=100}} \right. \left \{ {{x=\frac{100}{t}} \atop {(x-15)(t+3)=100}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx%3D%5Cfrac%7B100%7D%7Bt%7D%7D%20%5Catop%20%7B%28x-15%29%28t%2B3%29%3D100%7D%7D%20%5Cright.)
подставим это уравнение во второе в системе уравнений:
![(\frac{100}{t}-15)(t+3)=100 (\frac{100}{t}-15)(t+3)=100](https://tex.z-dn.net/?f=%28%5Cfrac%7B100%7D%7Bt%7D-15%29%28t%2B3%29%3D100)
![(\frac{100-15t}{t})(t+3)=100 (\frac{100-15t}{t})(t+3)=100](https://tex.z-dn.net/?f=%28%5Cfrac%7B100-15t%7D%7Bt%7D%29%28t%2B3%29%3D100)
(100-15t)(t+3)=100t;
100t+300-15t^2-45t-100t=0;
-15t^2-45t+300=0;
-t^2-3t+20=0;
t1 = 3 - √89 2·(-1) ≈ 3.2170
t2 = 3 + √89 2·(-1) ≈ -6.2170 ∅
x=100/3.2170=31,1км/ч скорость велика