Question Number 201433 by necx122 last updated on 06/Dec/23
$${A}\:{truck},\:{P},\:{travelling}\:{at}\:\mathrm{54}{km}/{h}\:{passes} \\ $$$${a}\:{point}\:{at}\:\mathrm{10}:\mathrm{30}\:{am}\:{while}\:{another}\:{truck}, \\ $$$${Q}\:{travelling}\:{at}\:\mathrm{90}{km}/{h}\:{passes}\:{through} \\ $$$${this}\:{same}\:{point}\:\mathrm{30}\:{minutes}\:{later}.\:{At} \\ $$$${what}\:{time}\:{will}\:{truck}\:{Q}\:{overtake}\:{P}? \\ $$
Answered by Rasheed.Sindhi last updated on 06/Dec/23
$${Let}\:{P}\:\:\&\:{Q}\:{meet}\:{after}\:{x}\:{hours} \\ $$$$\:{of}\:\mathrm{10}:\mathrm{30} \\ $$$$\begin{array}{|c|c|c|c|}{\:}&\hline{{P}}&\hline{{Q}}\\{{time}\left({in}\:{hours}\right)}&\hline{{x}}&\hline{{x}−\mathrm{1}/\mathrm{2}}\\{{speed}\left({km}/{h}\right)}&\hline{\mathrm{54}}&\hline{\mathrm{90}}\\{\underset{={speed}×{time}} {{Distance}\left({km}\right)}}&\hline{\mathrm{54}{x}}&\hline{\mathrm{90}{x}−\mathrm{45}}\\\hline\end{array} \\ $$$$\mathrm{54}{x}=\mathrm{90}{x}−\mathrm{45}\: \\ $$$$\mathrm{36}{x}=\mathrm{45}\Rightarrow{x}=\mathrm{45}/\mathrm{36}=\mathrm{5}/\mathrm{4}\:=\mathrm{1}\:{hour}\:\&\:\mathrm{15}\:{minutes} \\ $$$${P}\:{and}\:{Q}\:{meet}\:{at}\:\mathrm{11}:\mathrm{45} \\ $$
Commented by necx122 last updated on 06/Dec/23
This is indeed a great approach.
Answered by mr W last updated on 06/Dec/23
$${at}\:\mathrm{11}:\mathrm{00}\:{am}\:{truck}\:{P}\:{is}\:\mathrm{0}.\mathrm{5}×\mathrm{54}=\mathrm{27} \\ $$$${km}\:{ahead}\:{of}\:{truck}\:{Q}.\:{to}\:{overtake}\:{P}, \\ $$$${Q}\:{needs}\:\frac{\mathrm{27}}{\mathrm{90}−\mathrm{54}}=\mathrm{0}.\mathrm{75}\:{h}=\mathrm{45}\:{min}. \\ $$$${that}\:{means}\:{at}\:\mathrm{11}:\mathrm{45}\:{am}\:{truck}\:{Q} \\ $$$${overtakes}\:{truck}\:{P}. \\ $$
Commented by necx122 last updated on 06/Dec/23
As usual, your analytical skills are always baffling. Thank you for this approach.
Answered by MathematicalUser2357 last updated on 06/Feb/24
$$“\boldsymbol{{Q}}\:{traveling}\:{at}\:\mathrm{90}{km}/{h}'' \\ $$$${You}'{re}\:{quoting}\:{the}\:{question}. \\ $$