Question

the speed of car is increased by 12 kilometre per hour it takes 40 minutes less to cover a distance of 240 kilometre find the original speed ?​

Answer 1

Gɪᴠᴇɴ:

• $\footnotesize\sf{The\:speed\:of\:car\:is\:increased\:by \:12\: kilometre \:per}$$\footnotesize\sf{hour\: it \:takes\: 40\: minutes\: less \:to \:cover \:a \:distance }$$\footnotesize\sf{of \:240\: kilometre \:find \:the\:original \:speed\:?}$

${ }$

Fɪɴᴅ:

• $\sf{The\:original\:speed\:of\:the\:car}$

${ }$

Sᴏʟᴜᴛɪᴏɴ:

• $\sf{The\:distance\:covered\:by\:the\:car\:\leadsto\:240\:km}$

$\underline{\bigstar\:\boldsymbol{Let's\:Consider}}$

• $\tt{\bold{``S\:km/hr"}}\:\dashrightarrow\:\footnotesize{represents\:the\:original}$$\footnotesize\sf{speed\:of\:the\:car}$

• $\sf{\bold{``(S\:+\:12)\:km/hr"}}\:\dashrightarrow\:\footnotesize{represents\:the}$$\footnotesize\sf{increased\:new\:speed\:of\:the\:car}$

${ }$

$\Large\sf{\bigstar{\pink{We\:Know\::}}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:{\underbrace{\blue{\mathfrak{Time\:\rightarrowtail\:{\frac{Distance}{Speed}}}}}}$

• $\footnotesize\sf{According\:to\:the\:question\:and\:the\:formula\:above,}$$\footnotesize\sf{we\:can\:from\:an\:equation\:as\::}$

${ }$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{\frac{240}{S}}\:-\:{\frac{240}{S\:+\:12}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{240\:[\:{\frac{1}{S}}\:-\:{\frac{1}{S\:+\:12}}\:=\:{\frac{2}{3}}\:]}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{\frac{1}{S}}\:-\:{\frac{1}{S\:+\:12}}\:=\:{\frac{1}{360}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{\frac{S\:+\:12\:-\:S}{S\:(S\:+\:12)}}\:=\:{\frac{1}{360}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{\frac{12}{S\:(S\:+\:12)}}\:=\:{\frac{1}{360}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{S}^{2}\:{+\:12S\:=\:4320}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{S}^{2}\:{+\:12S\:-\:4320\:=\:0}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{S}^{2}\:{+\:72S\:-\:60S\:-\:4320\:=\:0}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{S\:(S\:+\:72)\:-\:60\:(S\:+\:72)}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{(S\:+\:72)\:(S\:-\:60)}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{S\:=\:-\:72\:;60}$

• $\footnotesize\sf{Since\:speed\:cannot\:be\:negative,\:so\:taking\:the}$$\footnotesize\sf{positive\:value\:of\:the\:speed}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\bf\:{S\:=\:60\:km/hr}$

${ }$

$\:\:\:\:\:\:\:\:{\bold{\purple{\dag}}}\:{\underline{\sf{The\:original\:speed\:of\:the\:car\:is\:{\bold{\mathfrak{\orange{60\:km/hr}}}}}}}.$