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There-are-two-possible-routes-from-Zindhi-to-Katifa-One-route-is-through-Zindhi-Chadler-expressway-which-is-100km-and-the-other-is-through-Adfeti-and-Ngonu-covering-a-distance-of-80km-A-motorist-goi




Question Number 202086 by necx122 last updated on 20/Dec/23
There are two possible routes from  Zindhi to Katifa. One route is through  Zindhi/Chadler expressway which is  100km and the other is through Adfeti and  Ngonu covering a distance of 80km. A  motorist going through the expressway  can travel 10km/h faster than the one  going through Adfeti and Ngonu, and  arrive Katifa 5 minutes earlier as well.  What is the time spent on the journey  to Katifa by the motorist travelling  through the expressway.
$${There}\:{are}\:{two}\:{possible}\:{routes}\:{from} \\ $$$${Zindhi}\:{to}\:{Katifa}.\:{One}\:{route}\:{is}\:{through} \\ $$$${Zindhi}/{Chadler}\:{expressway}\:{which}\:{is} \\ $$$$\mathrm{100}{km}\:{and}\:{the}\:{other}\:{is}\:{through}\:{Adfeti}\:{and} \\ $$$${Ngonu}\:{covering}\:{a}\:{distance}\:{of}\:\mathrm{80}{km}.\:{A} \\ $$$${motorist}\:{going}\:{through}\:{the}\:{expressway} \\ $$$${can}\:{travel}\:\mathrm{10}{km}/{h}\:{faster}\:{than}\:{the}\:{one} \\ $$$${going}\:{through}\:{Adfeti}\:{and}\:{Ngonu},\:{and} \\ $$$${arrive}\:{Katifa}\:\mathrm{5}\:{minutes}\:{earlier}\:{as}\:{well}. \\ $$$${What}\:{is}\:{the}\:{time}\:{spent}\:{on}\:{the}\:{journey} \\ $$$${to}\:{Katifa}\:{by}\:{the}\:{motorist}\:{travelling} \\ $$$${through}\:{the}\:{expressway}. \\ $$
Answered by mr W last updated on 20/Dec/23
((100)/t)=((80)/(t+(1/(12))))+10  12t^2 −23t−10=0  t=((23+(√(1009)))/(24))≈2.28 h=2h16m
$$\frac{\mathrm{100}}{{t}}=\frac{\mathrm{80}}{{t}+\frac{\mathrm{1}}{\mathrm{12}}}+\mathrm{10} \\ $$$$\mathrm{12}{t}^{\mathrm{2}} −\mathrm{23}{t}−\mathrm{10}=\mathrm{0} \\ $$$${t}=\frac{\mathrm{23}+\sqrt{\mathrm{1009}}}{\mathrm{24}}\approx\mathrm{2}.\mathrm{28}\:{h}=\mathrm{2}{h}\mathrm{16}{m} \\ $$
Commented by necx122 last updated on 20/Dec/23
This too is clear. Thank you so much sir.

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