Question Number 208637 by efronzo1 last updated on 20/Jun/24
$$\:\:\:{s} \\ $$
Answered by Berbere last updated on 20/Jun/24
$${find}\:{fractin}\:{that}\:{one}\:{man}\:{can}\:{compete}\:{per}\:{day}\:{V}_{{m}} \\ $$$${and}\:{women}\:{V}_{{w}} \\ $$$${V}_{{m}} =\frac{\mathrm{1}}{\mathrm{16}.\mathrm{24}} \\ $$$${V}_{{w}} =\frac{\mathrm{1}}{\mathrm{16}.\mathrm{48}} \\ $$$${so}\:{it}\:{just}\:{find}\:{x}\:; \\ $$$$\mathrm{14}.\mathrm{12}.{V}_{{m}} +{x}\left(\mathrm{12}{V}_{{m}} +\mathrm{12}{V}_{{w}} \right)=\mathrm{1} \\ $$$${x}.\left(\frac{\mathrm{1}}{\mathrm{32}}+\frac{\mathrm{1}}{\mathrm{64}}\right)=\frac{\mathrm{9}}{\mathrm{16}}\Rightarrow{x}=\mathrm{4} \\ $$$${Total}\:\mathrm{14}+\mathrm{4}=\mathrm{18} \\ $$
Commented by efronzo1 last updated on 20/Jun/24
$$\mathrm{x}\:=\:\mathrm{12} \\ $$
Answered by A5T last updated on 20/Jun/24
$${In}\:\mathrm{1}\:{day},\:{the}\:\mathrm{48}\:{women}\:{did}\:\frac{\mathrm{1}}{\mathrm{16}}\:{of}\:{the}\:{job} \\ $$$$\Rightarrow\mathrm{1}\:{woman}\:{did}\:\frac{\mathrm{1}}{\mathrm{16}×\mathrm{48}}\:{of}\:{the}\:{job}\:{per}\:{day} \\ $$$${Similarly},\:\mathrm{1}\:{man}\:{would}\:{do}\:\frac{\mathrm{1}}{\mathrm{16}×\mathrm{24}}\:{per}\:{day} \\ $$$$\left(\mathrm{12}×\frac{\mathrm{1}}{\mathrm{16}×\mathrm{24}}×\mathrm{14}\right)+{x}\left(\frac{\mathrm{12}}{\mathrm{16}×\mathrm{24}}+\frac{\mathrm{12}}{\mathrm{16}×\mathrm{48}}\right)=\mathrm{1} \\ $$$$\Rightarrow{x}=\mathrm{12} \\ $$
Answered by MM42 last updated on 20/Jun/24
$$\frac{\mathrm{16}×\mathrm{48}}{\mathrm{16}×\mathrm{24}}=\mathrm{2}\Rightarrow{m}=\mathrm{2}{w} \\ $$$$\Rightarrow{number}\:{of}\:{days}\:{to}\:{with}\:\mathrm{12}\:{mens} \\ $$$$\mathrm{16}×\mathrm{24}=\mathrm{12}×{x}\Rightarrow{x}=\mathrm{32} \\ $$$${the}\:{remaining}\:{days}\:{of}\:{doing}\:{work}\:{with}\:\mathrm{12}\:{mens} \\ $$$$\mathrm{32}−\mathrm{14}=\mathrm{18} \\ $$$$\:\mathrm{12}\:{m}\:\&\:\mathrm{12}\:{w}\:\equiv\:\mathrm{18}\:{m} \\ $$$$\Rightarrow\mathrm{12}×\mathrm{18}=\mathrm{18}×{x}\Rightarrow{x}=\mathrm{12}\:\checkmark \\ $$$$ \\ $$