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Question Number 8564 by tawakalitu last updated on 16/Oct/16

Commented by ridwan balatif last updated on 16/Oct/16

$$\mathrm{let}:{\mathrm{V}}^{\prime }={\mathrm{V}}_{\mathrm{o}}-4,\mathrm{with}{\mathrm{V}}_{\mathrm{o}}\mathrm{is}\mathrm{speed}\mathrm{that}\mathrm{we}\mathrm{want}\mathrm{to}\mathrm{count}\mathrm{it}$$$${\mathrm{t}}^{{}^{\prime }}=\mathrm{t}+2$$$$\mathrm{S}=240\mathrm{km}$$$${\mathrm{S}}^{\prime }=240\mathrm{km}$$$$\mathrm{S}={\mathrm{S}}^{\prime }$$$${\mathrm{V}}_{\mathrm{o}}.\mathrm{t}={\mathrm{V}}^{\prime }.{\mathrm{t}}^{\prime }$$$${\mathrm{V}}_{\mathrm{o}}.\mathrm{t}=({\mathrm{V}}_{\mathrm{o}}-4).(\mathrm{t}+2)$$$${\mathrm{V}}_{\mathrm{o}}.\mathrm{t}={\mathrm{V}}_{\mathrm{o}}.\mathrm{t}+{2\mathrm{V}}_{\mathrm{o}}-4\mathrm{t}-8$$$$0={2\mathrm{V}}_{\mathrm{o}}-4\mathrm{t}-8$$$$4\mathrm{t}+8={2\mathrm{V}}_{\mathrm{o}}$$$${\mathrm{V}}_{\mathrm{o}}=2\mathrm{t}+4...\left(1\right)$$$$\mathrm{S}={\mathrm{V}}_{\mathrm{o}}.\mathrm{t}$$$$240={\mathrm{V}}_{\mathrm{o}}.\mathrm{t}...\left(2\right)$$$$\left(1\right)\to \left(2\right)$$$$240=(2\mathrm{t}+4).\mathrm{t}$$$$120={\mathrm{t}}^2+2\mathrm{t}$$$$0={\mathrm{t}}^2+2\mathrm{t}-120$$$$0=(\mathrm{t}-10)(\mathrm{t}+12)$$$$\mathrm{t}=10\mathrm{hours}\mathrm{t}=-12\mathrm{hours}\left(\mathrm{IMPOSSIBLE}\right)$$$$\mathrm{use}\mathrm{t}=10\mathrm{hours},\mathrm{we}\mathrm{get}$$$$240={\mathrm{V}}_{\mathrm{o}}.\mathrm{t}$$$$240={\mathrm{V}}_{\mathrm{o}}.10$$$${\mathrm{V}}_{\mathrm{o}}=24\mathrm{km}/\mathrm{hours}$$$$\mathrm{sorry}\mathrm{if}\mathrm{my}\mathrm{English}\mathrm{is}\mathrm{bad}$$

Commented by tawakalitu last updated on 16/Oct/16

$$\mathrm{Thanks}\mathrm{so}\mathrm{much}.$$

Commented by ridwan balatif last updated on 16/Oct/16

$$\mathrm{your}\mathrm{welcome}$$

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