The distance between two trucks moving towards each other is decreasing at the rate of $10{\mathrm{ms}}^{-1}\text{. }$ If these trucks travel with same speeds in same direction the separation increases at the rate of $5 {\mathrm{ms}}^{-1}$. The speeds of the trucks are :

According to the given equation First case: Separation between the trucks decreases at the rate of $10{\mathrm{ms}}^{-1}\text{. }$ Due to the opposite relative motion of trucks away from each other V₁ + V₂ = 10 (condition given) …… (1) Seconds case: Separation between the trucks increases due to the opposite relative motion of trucks away from each other

${\mathrm{V}}_1-{\mathrm{V}}_2=5\dots \dots \left(2\right)\text{ (condition given) }$

From equation (1) and (2), we get

${\mathrm{V}}_1+{\mathrm{V}}_2=10\dots \left(\mathrm{i}\right)$

${\mathrm{V}}_1-{\mathrm{V}}_2=5\dots \text{ (ii) }$

${\mathrm{Eq}}^{\mathrm{n}}\left(\mathrm{i}\right)+\left(\mathrm{ii}\right)$

$2V_1=15$

$V_1=7.5{\mathrm{ms}}^{-1}$

$\mathrm{Eqn}\left(\mathrm{i}\right)-\left(\mathrm{ii}\right)$

$2V_2=5$

$V_2=2.5{\mathrm{ms}}^{-1}$