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Question Number 208637 by efronzo1 last updated on 20/Jun/24

   s

$$\:\:\:{s} \\ $$

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 =(1/(16.24))  V_w =(1/(16.48))  so it just find x ;  14.12.V_m +x(12V_m +12V_w )=1  x.((1/(32))+(1/(64)))=(9/(16))⇒x=4  Total 14+4=18

$${find}\:{fractin}\:{that}\:{one}\:{man}\:{can}\:{compete}\:{per}\:{day}\:{V}_{{m}} \\ $$$${and}\:{women}\:{V}_{{w}} \\ $$$${V}_{{m}} =\frac{\mathrm{1}}{\mathrm{16}.\mathrm{24}} \\ $$$${V}_{{w}} =\frac{\mathrm{1}}{\mathrm{16}.\mathrm{48}} \\ $$$${so}\:{it}\:{just}\:{find}\:{x}\:; \\ $$$$\mathrm{14}.\mathrm{12}.{V}_{{m}} +{x}\left(\mathrm{12}{V}_{{m}} +\mathrm{12}{V}_{{w}} \right)=\mathrm{1} \\ $$$${x}.\left(\frac{\mathrm{1}}{\mathrm{32}}+\frac{\mathrm{1}}{\mathrm{64}}\right)=\frac{\mathrm{9}}{\mathrm{16}}\Rightarrow{x}=\mathrm{4} \\ $$$${Total}\:\mathrm{14}+\mathrm{4}=\mathrm{18} \\ $$

Commented by efronzo1 last updated on 20/Jun/24

x = 12

$$\mathrm{x}\:=\:\mathrm{12} \\ $$

Answered by A5T last updated on 20/Jun/24

In 1 day, the 48 women did (1/(16)) of the job  ⇒1 woman did (1/(16×48)) of the job per day  Similarly, 1 man would do (1/(16×24)) per day  (12×(1/(16×24))×14)+x(((12)/(16×24))+((12)/(16×48)))=1  ⇒x=12

$${In}\:\mathrm{1}\:{day},\:{the}\:\mathrm{48}\:{women}\:{did}\:\frac{\mathrm{1}}{\mathrm{16}}\:{of}\:{the}\:{job} \\ $$$$\Rightarrow\mathrm{1}\:{woman}\:{did}\:\frac{\mathrm{1}}{\mathrm{16}×\mathrm{48}}\:{of}\:{the}\:{job}\:{per}\:{day} \\ $$$${Similarly},\:\mathrm{1}\:{man}\:{would}\:{do}\:\frac{\mathrm{1}}{\mathrm{16}×\mathrm{24}}\:{per}\:{day} \\ $$$$\left(\mathrm{12}×\frac{\mathrm{1}}{\mathrm{16}×\mathrm{24}}×\mathrm{14}\right)+{x}\left(\frac{\mathrm{12}}{\mathrm{16}×\mathrm{24}}+\frac{\mathrm{12}}{\mathrm{16}×\mathrm{48}}\right)=\mathrm{1} \\ $$$$\Rightarrow{x}=\mathrm{12} \\ $$

Answered by MM42 last updated on 20/Jun/24

((16×48)/(16×24))=2⇒m=2w  ⇒number of days to with 12 mens  16×24=12×x⇒x=32  the remaining days of doing work with 12 mens  32−14=18   12 m & 12 w ≡ 18 m  ⇒12×18=18×x⇒x=12 ✓

$$\frac{\mathrm{16}×\mathrm{48}}{\mathrm{16}×\mathrm{24}}=\mathrm{2}\Rightarrow{m}=\mathrm{2}{w} \\ $$$$\Rightarrow{number}\:{of}\:{days}\:{to}\:{with}\:\mathrm{12}\:{mens} \\ $$$$\mathrm{16}×\mathrm{24}=\mathrm{12}×{x}\Rightarrow{x}=\mathrm{32} \\ $$$${the}\:{remaining}\:{days}\:{of}\:{doing}\:{work}\:{with}\:\mathrm{12}\:{mens} \\ $$$$\mathrm{32}−\mathrm{14}=\mathrm{18} \\ $$$$\:\mathrm{12}\:{m}\:\&\:\mathrm{12}\:{w}\:\equiv\:\mathrm{18}\:{m} \\ $$$$\Rightarrow\mathrm{12}×\mathrm{18}=\mathrm{18}×{x}\Rightarrow{x}=\mathrm{12}\:\checkmark \\ $$$$ \\ $$

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