Respuesta :
Let's say that the two cars travel from city A to city B, and we know that AB = 500m.
Let's also say that we consider city A to sit at x = 0, and city B to sit at x = 500. So, speed is positive for the car going from A to B, and is negative for the car going from B to A.
So, the first car follows this rule:
[tex] s_1 = v_1t [/tex]
While the second car follows this rule:
[tex] s_2 = 500 - v_2t [/tex]
But we know that the difference between their speed is 40, so let's say that
[tex] v2 = v1+40 \implies s_2 = 500 - (v_1+40)t [/tex]
These are the equations that identify the position of the cars after [tex] t [/tex] hours. Since we know that after 5 hours (i.e. [tex] t = 5 [/tex]) the cars meet, it means that if we plug that value in both equations, we will have the same results. In formulas,
[tex] 5v_1 = 500 - 5(v_1+40) [/tex]
From here, it's easy to rearrange the equation and solve for the first car's speed:
[tex] 5v_1 = 500 - 5v_1+200 [/tex]
[tex] 5v_1 = 700 - 5v_1 [/tex]
[tex] 10v_1 = 700 [/tex]
[tex] v_1 = 70 [/tex]
And since the speed of the second car was 40 more than the first one, we have
[tex] v_2 = v_1 + 40 = 70 + 40 = 110 [/tex]
