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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

let: V′=V_o −4 , with V_o is speed that we want to count it t^′ =t+2 S =240 km S′=240km S=S′ V_o .t=V′.t′ V_o .t=(V_o −4).(t+2) V_o .t=V_o .t+2V_o −4t−8 0=2V_o −4t−8 4t+8=2V_o V_o =2t+4...(1) S=V_o .t 240=V_o .t...(2) (1)→(2) 240=(2t+4).t 120=t^2 +2t 0=t^2 +2t−120 0=(t−10)(t+12) t=10hours t=−12hours(IMPOSSIBLE) use t=10 hours, we get 240=V_o .t 240=V_o .10 V_o =24 km/hours sorry if my English is bad

$$\mathrm{let}:\:\mathrm{V}'=\mathrm{V}_{\mathrm{o}} −\mathrm{4}\:,\:\:\:\mathrm{with}\:\mathrm{V}_{\mathrm{o}} \:\mathrm{is}\:\mathrm{speed}\:\mathrm{that}\:\mathrm{we}\:\mathrm{want}\:\mathrm{to}\:\mathrm{count}\:\mathrm{it} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{t}^{'} \:=\mathrm{t}+\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{S}\:=\mathrm{240}\:\mathrm{km} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{S}'=\mathrm{240km} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{S}=\mathrm{S}' \\ $$$$\mathrm{V}_{\mathrm{o}} .\mathrm{t}=\mathrm{V}'.\mathrm{t}' \\ $$$$\mathrm{V}_{\mathrm{o}} .\mathrm{t}=\left(\mathrm{V}_{\mathrm{o}} −\mathrm{4}\right).\left(\mathrm{t}+\mathrm{2}\right) \\ $$$$\mathrm{V}_{\mathrm{o}} .\mathrm{t}=\mathrm{V}_{\mathrm{o}} .\mathrm{t}+\mathrm{2V}_{\mathrm{o}} −\mathrm{4t}−\mathrm{8} \\ $$$$\mathrm{0}=\mathrm{2V}_{\mathrm{o}} −\mathrm{4t}−\mathrm{8} \\ $$$$\mathrm{4t}+\mathrm{8}=\mathrm{2V}_{\mathrm{o}} \\ $$$$\mathrm{V}_{\mathrm{o}} =\mathrm{2t}+\mathrm{4}...\left(\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\mathrm{S}=\mathrm{V}_{\mathrm{o}} .\mathrm{t} \\ $$$$\mathrm{240}=\mathrm{V}_{\mathrm{o}} .\mathrm{t}...\left(\mathrm{2}\right) \\ $$$$\left(\mathrm{1}\right)\rightarrow\left(\mathrm{2}\right) \\ $$$$\mathrm{240}=\left(\mathrm{2t}+\mathrm{4}\right).\mathrm{t} \\ $$$$\mathrm{120}=\mathrm{t}^{\mathrm{2}} +\mathrm{2t} \\ $$$$\:\:\:\:\:\:\mathrm{0}=\mathrm{t}^{\mathrm{2}} +\mathrm{2t}−\mathrm{120} \\ $$$$\:\:\:\:\:\:\mathrm{0}=\left(\mathrm{t}−\mathrm{10}\right)\left(\mathrm{t}+\mathrm{12}\right) \\ $$$$\:\:\mathrm{t}=\mathrm{10hours}\:\:\:\:\mathrm{t}=−\mathrm{12hours}\left(\mathrm{IMPOSSIBLE}\right) \\ $$$$\mathrm{use}\:\mathrm{t}=\mathrm{10}\:\mathrm{hours},\:\mathrm{we}\:\mathrm{get} \\ $$$$\mathrm{240}=\mathrm{V}_{\mathrm{o}} .\mathrm{t} \\ $$$$\mathrm{240}=\mathrm{V}_{\mathrm{o}} .\mathrm{10} \\ $$$$\mathrm{V}_{\mathrm{o}} \:\:=\mathrm{24}\:\mathrm{km}/\mathrm{hours} \\ $$$$\mathrm{sorry}\:\mathrm{if}\:\mathrm{my}\:\mathrm{English}\:\mathrm{is}\:\mathrm{bad} \\ $$

Commented by tawakalitu last updated on 16/Oct/16

Thanks so much.

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

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

your welcome

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

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