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Question Number 95277 by bobhans last updated on 24/May/20
Commented by mr W last updated on 24/May/20
((15)/(10×10))+(6/(12×10))=(1/x) x=5 days
$$\frac{\mathrm{15}}{\mathrm{10}×\mathrm{10}}+\frac{\mathrm{6}}{\mathrm{12}×\mathrm{10}}=\frac{\mathrm{1}}{{x}} \\ $$$${x}=\mathrm{5}\:{days} \\ $$
Commented by bobhans last updated on 24/May/20
sir why your method not correct to eq 95232?
$$\mathrm{sir}\:\mathrm{why}\:\mathrm{your}\:\mathrm{method}\:\mathrm{not}\:\mathrm{correct}\:\mathrm{to}\:\mathrm{eq}\:\mathrm{95232}? \\ $$
Commented by mr W last updated on 24/May/20
in 85232 i saw there was need to treat the problem from the ground, therefore i began with lesson one. but now we are in lesson ten, so we don′t need to do like in lesson one. main thing: we have understood and the answer is correct.
$${in}\:\mathrm{85232}\:{i}\:{saw}\:{there}\:{was}\:{need}\:{to}\: \\ $$$${treat}\:{the}\:{problem}\:{from}\:{the}\:{ground}, \\ $$$${therefore}\:{i}\:{began}\:{with}\:{lesson}\:{one}.\:{but} \\ $$$${now}\:{we}\:{are}\:{in}\:{lesson}\:{ten},\:{so}\:{we}\:{don}'{t} \\ $$$${need}\:{to}\:{do}\:{like}\:{in}\:{lesson}\:{one}.\:{main} \\ $$$${thing}:\:{we}\:{have}\:{understood}\:{and}\:{the} \\ $$$${answer}\:{is}\:{correct}. \\ $$
Commented by i jagooll last updated on 24/May/20
i have the problem like that. i will post
$$\mathrm{i}\:\mathrm{have}\:\mathrm{the}\:\mathrm{problem}\:\mathrm{like}\:\mathrm{that}.\:\mathrm{i}\:\mathrm{will} \\ $$$$\mathrm{post} \\ $$
Answered by i jagooll last updated on 24/May/20
say 10m×10 = s 12w×10 = s { ((100m=120w)),((m=(6/5)w)) :} then (15m+6w).x = s ⇒(15×(6/5)w+6w)x = s (24w)x = s ⇒x = (s/(24w)) ...(i) from w = (s/(120)) ⇒ x = (s/(24×((s/(120))))) x = ((120)/(24)) = 5 days
$$\mathrm{say}\:\mathrm{10m}×\mathrm{10}\:=\:\mathrm{s} \\ $$$$\mathrm{12w}×\mathrm{10}\:=\:\mathrm{s}\:\begin{cases}{\mathrm{100m}=\mathrm{120w}}\\{\mathrm{m}=\frac{\mathrm{6}}{\mathrm{5}}\mathrm{w}}\end{cases} \\ $$$$\mathrm{then}\:\left(\mathrm{15m}+\mathrm{6w}\right).{x}\:=\:\mathrm{s} \\ $$$$\Rightarrow\left(\mathrm{15}×\frac{\mathrm{6}}{\mathrm{5}}\mathrm{w}+\mathrm{6w}\right){x}\:=\:\mathrm{s} \\ $$$$\left(\mathrm{24w}\right){x}\:=\:\mathrm{s}\:\Rightarrow{x}\:=\:\frac{\mathrm{s}}{\mathrm{24w}}\:…\left(\mathrm{i}\right) \\ $$$$\mathrm{from}\:\mathrm{w}\:=\:\frac{\mathrm{s}}{\mathrm{120}}\:\Rightarrow\:{x}\:=\:\frac{\mathrm{s}}{\mathrm{24}×\left(\frac{\mathrm{s}}{\mathrm{120}}\right)} \\ $$$${x}\:=\:\frac{\mathrm{120}}{\mathrm{24}}\:=\:\mathrm{5}\:{days} \\ $$$$ \\ $$
Commented by bobhans last updated on 24/May/20
dear prof mr w. please check my answer
$$\mathrm{dear}\:\mathrm{prof}\:\mathrm{mr}\:\mathrm{w}.\:\mathrm{please}\:\mathrm{check}\:\mathrm{my}\:\mathrm{answer} \\ $$
Commented by mr W last updated on 24/May/20
if your answer is also “5 days”, then correct.
$${if}\:{your}\:{answer}\:{is}\:{also}\:“\mathrm{5}\:{days}'',\:{then} \\ $$$${correct}. \\ $$
Commented by mr W last updated on 24/May/20
we can also solve it just using logic. 10 men in 10 days do the same as 12 women in 10 days, that means a man is so much as 1.2 women. 15 men and 6 women are the same as 15×1.2+6=24 women. so the question is how long need 24 women? since 12 women need 10 days, so 24 women need 5 days. this is the answer which you can also get even you don′t know how to solve equations.
$${we}\:{can}\:{also}\:{solve}\:{it}\:{just}\:{using}\:{logic}. \\ $$$$\mathrm{10}\:{men}\:{in}\:\mathrm{10}\:{days}\:{do}\:{the}\:{same}\:{as} \\ $$$$\mathrm{12}\:{women}\:{in}\:\mathrm{10}\:{days},\:{that}\:{means} \\ $$$${a}\:{man}\:{is}\:{so}\:{much}\:{as}\:\mathrm{1}.\mathrm{2}\:{women}. \\ $$$$\mathrm{15}\:{men}\:{and}\:\mathrm{6}\:{women}\:{are}\:{the}\:{same} \\ $$$${as}\:\mathrm{15}×\mathrm{1}.\mathrm{2}+\mathrm{6}=\mathrm{24}\:{women}.\:{so}\:{the} \\ $$$${question}\:{is}\:{how}\:{long}\:{need}\:\mathrm{24}\:{women}? \\ $$$${since}\:\mathrm{12}\:{women}\:{need}\:\mathrm{10}\:{days},\:{so}\:\mathrm{24} \\ $$$${women}\:{need}\:\mathrm{5}\:{days}.\:{this}\:{is}\:{the}\:{answer} \\ $$$${which}\:{you}\:{can}\:{also}\:{get}\:{even}\:{you}\:{don}'{t} \\ $$$${know}\:{how}\:{to}\:{solve}\:{equations}. \\ $$
Commented by bobhans last updated on 24/May/20
my method same with your answer 10 men →10 day 12women →10 day 15 men + 6 women →x day (1/x) = ((15)/(10×10)) + (6/(12×10)) but i compare to qn 95232 why not correct
$$\mathrm{my}\:\mathrm{method}\:\mathrm{same}\:\mathrm{with}\:\mathrm{your}\:\mathrm{answer} \\ $$$$\mathrm{10}\:\mathrm{men}\:\rightarrow\mathrm{10}\:\mathrm{day} \\ $$$$\mathrm{12women}\:\rightarrow\mathrm{10}\:\mathrm{day} \\ $$$$\mathrm{15}\:\mathrm{men}\:+\:\mathrm{6}\:\mathrm{women}\:\rightarrow\mathrm{x}\:\mathrm{day} \\ $$$$\frac{\mathrm{1}}{\mathrm{x}}\:=\:\frac{\mathrm{15}}{\mathrm{10}×\mathrm{10}}\:+\:\frac{\mathrm{6}}{\mathrm{12}×\mathrm{10}} \\ $$$$\mathrm{but}\:\mathrm{i}\:\mathrm{compare}\:\mathrm{to}\:\mathrm{qn}\:\mathrm{95232}\:\mathrm{why}\:\mathrm{not}\:\mathrm{correct} \\ $$
Answered by Farruxjano last updated on 24/May/20
Solution: Let: the man′s speed−v_1 , the woman′s speed−v_2 , the work−S. So, we get from the the task: 10v_1 =(S/(10)) ⇒ v_1 =(S/(100)) and 12v_2 =(S/(10)) ⇒ v_2 =(S/(120)) we must calculate: 15v_1 +6v_2 = =15∙(S/(100))+6∙(S/(120))=((3S)/(20))+(S/(20))=((4S)/(20))=(S/5) But: (S/5)<S ⇒ So, they don′t cope!
$$\boldsymbol{{Solution}}:\:\boldsymbol{{Let}}:\:\boldsymbol{{the}}\:\boldsymbol{{man}}'\boldsymbol{{s}}\:\boldsymbol{{speed}}−\boldsymbol{{v}}_{\mathrm{1}} , \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{woman}}'\boldsymbol{{s}}\:\boldsymbol{{speed}}−\boldsymbol{{v}}_{\mathrm{2}} ,\:\boldsymbol{{the}}\:\boldsymbol{{work}}−\boldsymbol{{S}}. \\ $$$$\boldsymbol{{So}},\:\boldsymbol{{we}}\:\boldsymbol{{get}}\:\boldsymbol{{from}}\:\boldsymbol{{the}}\:\boldsymbol{{the}}\:\boldsymbol{{task}}: \\ $$$$\mathrm{10}\boldsymbol{{v}}_{\mathrm{1}} =\frac{\boldsymbol{{S}}}{\mathrm{10}}\:\Rightarrow\:\boldsymbol{{v}}_{\mathrm{1}} =\frac{\boldsymbol{{S}}}{\mathrm{100}}\:\boldsymbol{{and}}\:\mathrm{12}\boldsymbol{{v}}_{\mathrm{2}} =\frac{\boldsymbol{{S}}}{\mathrm{10}}\:\Rightarrow\:\boldsymbol{{v}}_{\mathrm{2}} =\frac{\boldsymbol{{S}}}{\mathrm{120}} \\ $$$$\boldsymbol{{we}}\:\boldsymbol{{must}}\:\boldsymbol{{calculate}}:\:\mathrm{15}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{6}\boldsymbol{{v}}_{\mathrm{2}} = \\ $$$$=\mathrm{15}\centerdot\frac{\boldsymbol{{S}}}{\mathrm{100}}+\mathrm{6}\centerdot\frac{\boldsymbol{{S}}}{\mathrm{120}}=\frac{\mathrm{3}\boldsymbol{{S}}}{\mathrm{20}}+\frac{\boldsymbol{{S}}}{\mathrm{20}}=\frac{\mathrm{4}\boldsymbol{{S}}}{\mathrm{20}}=\frac{\boldsymbol{{S}}}{\mathrm{5}}\:\boldsymbol{{But}}: \\ $$$$\frac{\boldsymbol{{S}}}{\mathrm{5}}<\boldsymbol{{S}}\:\:\:\:\:\:\Rightarrow\:\:\:\:\:\:\boldsymbol{{So}},\:\boldsymbol{{they}}\:\boldsymbol{{don}}'\boldsymbol{{t}}\:\boldsymbol{{cope}}! \\ $$
Commented by bobhans last updated on 24/May/20
what the meaning don′t cope?
$$\mathrm{what}\:\mathrm{the}\:\mathrm{meaning}\:\mathrm{don}'\mathrm{t}\:\mathrm{cope}? \\ $$
Commented by Farruxjano last updated on 24/May/20
They cannot complete in time! sorry I said that i don′t know English perfect :)
$$\boldsymbol{{They}}\:\boldsymbol{{cannot}}\:\boldsymbol{{complete}}\:\boldsymbol{{in}}\:\boldsymbol{{time}}! \\ $$$$\boldsymbol{{sorry}}\:\boldsymbol{{I}}\:\boldsymbol{{said}}\:\boldsymbol{{that}}\:\boldsymbol{{i}}\:\boldsymbol{{don}}'\boldsymbol{{t}}\:\boldsymbol{{know}}\:\boldsymbol{{English}} \\ $$$$\left.\boldsymbol{{perfect}}\::\right) \\ $$
Commented by mr W last updated on 24/May/20
even with only one man or one woman the job can be finished, that′s for sure. it′s only a question how long they need. so what do you mean with “they can not complete in time”?
$${even}\:{with}\:{only}\:{one}\:{man}\:{or}\:{one}\:{woman} \\ $$$${the}\:{job}\:{can}\:{be}\:{finished},\:{that}'{s}\:{for}\:{sure}. \\ $$$${it}'{s}\:{only}\:{a}\:{question}\:{how}\:{long}\:{they}\:{need}. \\ $$$${so}\:{what}\:{do}\:{you}\:{mean}\:{with}\:“{they}\:{can} \\ $$$${not}\:{complete}\:{in}\:{time}''? \\ $$

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