Question and Answers Forum

All Questions      Topic List

Arithmetic Questions

Previous in All Question      Next in All Question      

Previous in Arithmetic      Next in Arithmetic      

Question Number 99011 by bemath last updated on 18/Jun/20

Commented by MJS last updated on 18/Jun/20

strange kind of question  the given answers 1, 2, 3 are one possible  solution but it′s not possible to find an  unique solution  (1/a)+(1/b)=(1/(16))  (1/b)+(1/c)=(1/(12))  (2/a)+(7/b)+(x/c)=1  [x=the time c needs to finish the work after    a worked 2 days and b worked 7 days]  with x as parameter we get  a=−((48(x−5))/(x−27))  b=((24(x−5))/(2x−21))  c=((24(x−5))/(11))  restrictions:  a>16∧b>16∧c>12 ⇒ ((21)/2)<x<27  if we set x=16 we get a=48∧b=c=24

$$\mathrm{strange}\:\mathrm{kind}\:\mathrm{of}\:\mathrm{question} \\ $$$$\mathrm{the}\:\mathrm{given}\:\mathrm{answers}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3}\:\mathrm{are}\:\mathrm{one}\:\mathrm{possible} \\ $$$$\mathrm{solution}\:\mathrm{but}\:\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{find}\:\mathrm{an} \\ $$$$\mathrm{unique}\:\mathrm{solution} \\ $$$$\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}=\frac{\mathrm{1}}{\mathrm{16}} \\ $$$$\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}=\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$\frac{\mathrm{2}}{{a}}+\frac{\mathrm{7}}{{b}}+\frac{{x}}{{c}}=\mathrm{1} \\ $$$$\left[{x}=\mathrm{the}\:\mathrm{time}\:{c}\:\mathrm{needs}\:\mathrm{to}\:\mathrm{finish}\:\mathrm{the}\:\mathrm{work}\:\mathrm{after}\right. \\ $$$$\left.\:\:{a}\:\mathrm{worked}\:\mathrm{2}\:\mathrm{days}\:\mathrm{and}\:{b}\:\mathrm{worked}\:\mathrm{7}\:\mathrm{days}\right] \\ $$$$\mathrm{with}\:{x}\:\mathrm{as}\:\mathrm{parameter}\:\mathrm{we}\:\mathrm{get} \\ $$$${a}=−\frac{\mathrm{48}\left({x}−\mathrm{5}\right)}{{x}−\mathrm{27}} \\ $$$${b}=\frac{\mathrm{24}\left({x}−\mathrm{5}\right)}{\mathrm{2}{x}−\mathrm{21}} \\ $$$${c}=\frac{\mathrm{24}\left({x}−\mathrm{5}\right)}{\mathrm{11}} \\ $$$$\mathrm{restrictions}: \\ $$$${a}>\mathrm{16}\wedge{b}>\mathrm{16}\wedge{c}>\mathrm{12}\:\Rightarrow\:\frac{\mathrm{21}}{\mathrm{2}}<{x}<\mathrm{27} \\ $$$$\mathrm{if}\:\mathrm{we}\:\mathrm{set}\:{x}=\mathrm{16}\:\mathrm{we}\:\mathrm{get}\:{a}=\mathrm{48}\wedge{b}={c}=\mathrm{24} \\ $$

Commented by bemath last updated on 18/Jun/20

waw..thanks mr Mjs

$$\mathrm{waw}..\mathrm{thanks}\:\mathrm{mr}\:\mathrm{Mjs} \\ $$

Answered by bobhans last updated on 18/Jun/20

(v_A +v_B )×16 = w  (v_B +v_C )×12 = w  2v_A +7v_B +t.v_C  = w   information on the problem is incomplete

$$\left(\mathrm{v}_{\mathrm{A}} +\mathrm{v}_{\mathrm{B}} \right)×\mathrm{16}\:=\:\mathrm{w} \\ $$$$\left(\mathrm{v}_{\mathrm{B}} +\mathrm{v}_{\mathrm{C}} \right)×\mathrm{12}\:=\:\mathrm{w} \\ $$$$\mathrm{2v}_{\mathrm{A}} +\mathrm{7v}_{\mathrm{B}} +\mathrm{t}.\mathrm{v}_{\mathrm{C}} \:=\:\mathrm{w}\: \\ $$$$\mathrm{information}\:\mathrm{on}\:\mathrm{the}\:\mathrm{problem}\:\mathrm{is}\:\mathrm{incomplete} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com