A-distance-of-200-km-is-to-be-covered-by-car-in-less-than-10-hours-Yash-does-it-in-two-parts-He-first-drives-for-150-km-at-an-average-speed-of-36-km-hr-without-stopping-After-taking-rest-for-30-mi

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Question Number 16942 by Tinkutara last updated on 28/Jun/17

$$\mathrm{A}\mathrm{distance}\mathrm{of}200\mathrm{km}\mathrm{is}\mathrm{to}\mathrm{be}\mathrm{covered}\mathrm{by}$$$$\mathrm{car}\mathrm{in}\mathrm{less}\mathrm{than}10\mathrm{hours}.\mathrm{Yash}\mathrm{does}\mathrm{it}$$$$\mathrm{in}\mathrm{two}\mathrm{parts}.\mathrm{He}\mathrm{first}\mathrm{drives}\mathrm{for}150\mathrm{km}$$$$\mathrm{at}\mathrm{an}\mathrm{average}\mathrm{speed}\mathrm{of}36\mathrm{km}/\mathrm{hr},$$$$\mathrm{without}\mathrm{stopping}.\mathrm{After}\mathrm{taking}\mathrm{rest}\mathrm{for}$$$$30\mathrm{minutes},\mathrm{he}\mathrm{starts}\mathrm{again}\mathrm{and}\mathrm{covers}$$$$\mathrm{the}\mathrm{remaining}\mathrm{distance}\mathrm{non}-\mathrm{stop}.\mathrm{His}$$$$\mathrm{average}\mathrm{for}\mathrm{the}\mathrm{entire}\mathrm{journey}$$$$\left(\mathrm{including}\mathrm{the}\mathrm{period}\mathrm{of}\mathrm{rest}\right)\mathrm{exceeds}$$$$\mathrm{that}\mathrm{for}\mathrm{the}\mathrm{second}\mathrm{part}\mathrm{by}5\mathrm{km}/\mathrm{hr}.$$$$\mathrm{Find}\mathrm{the}\mathrm{speed}\mathrm{at}\mathrm{which}\mathrm{he}\mathrm{covers}\mathrm{the}$$$$\mathrm{second}\mathrm{part}.$$

Answered by mrW1 last updated on 29/Jun/17

$$\frac{200}{\frac{150}{36}+0.5+\frac{50}{\mathrm{x}}}=\mathrm{x}+5$$$$\frac{200\times 36\mathrm{x}}{168\mathrm{x}+1800}=\mathrm{x}+5$$$${168\mathrm{x}}^2+1800\mathrm{x}+840\mathrm{x}+9000-7200\mathrm{x}=0$$$${168\mathrm{x}}^2-4560\mathrm{x}+9000=0$$$${7\mathrm{x}}^2-190\mathrm{x}+375=0$$$$\mathrm{x}=\frac{190\pm \sqrt{{190}^2-4\times 7\times 375}}{2\times 7}=\frac{190\pm 160}{14}$$$$\Rightarrow {\mathrm{x}}_1=\frac{190-160}{14}=2.14\left(\mathrm{not}\mathrm{suitable}\right)$$$$\Rightarrow {\mathrm{x}}_2=\frac{190+160}{14}=25\mathrm{km}/\mathrm{h}\left(\mathrm{ok}\right)$$

Commented by Tinkutara last updated on 29/Jun/17

$$\mathrm{Thanks}\mathrm{Sir}!$$

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