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A-can-do-a-work-in-10-days-and-B-can-do-the-same-work-in-15-days-How-many-days-will-they-take-if-both-work-together-

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Question Number 9167 by nazar last updated on 21/Nov/16
A can do a work in 10 days and B can do the same work in 15 days. How many days will they take if both work together?
$$\mathrm{A}\:\mathrm{can}\:\mathrm{do}\:\mathrm{a}\:\mathrm{work}\:\mathrm{in}\:\mathrm{10}\:\mathrm{days}\:\mathrm{and}\:\mathrm{B}\:\mathrm{can} \\ $$$$\mathrm{do}\:\mathrm{the}\:\mathrm{same}\:\mathrm{work}\:\mathrm{in}\:\mathrm{15}\:\mathrm{days}.\:\mathrm{How}\: \\ $$$$\mathrm{many}\:\mathrm{days}\:\mathrm{will}\:\mathrm{they}\:\mathrm{take}\:\mathrm{if}\:\:\mathrm{both}\:\mathrm{work} \\ $$$$\mathrm{together}? \\ $$
Commented by tawakalitu last updated on 22/Nov/16
Let the time it take both of them be = x ∴ x((1/(10)) + (1/(15))) = 1 ∴ x(((15 + 10)/(150))) = 1 ∴ x(((25)/(150))) = 1 ∴ x((1/6)) = 1 ∴ (x/6) = 1 Cross multiply ∴ x = 6 Hence it will take both of them 6 days to finish the work if they both work together. DONE !
$$\mathrm{Let}\:\mathrm{the}\:\mathrm{time}\:\mathrm{it}\:\mathrm{take}\:\mathrm{both}\:\mathrm{of}\:\mathrm{them}\:\mathrm{be}\:=\:\mathrm{x} \\ $$$$\therefore\:\:\mathrm{x}\left(\frac{\mathrm{1}}{\mathrm{10}}\:+\:\frac{\mathrm{1}}{\mathrm{15}}\right)\:=\:\mathrm{1} \\ $$$$\therefore\:\:\mathrm{x}\left(\frac{\mathrm{15}\:+\:\mathrm{10}}{\mathrm{150}}\right)\:=\:\mathrm{1} \\ $$$$\therefore\:\:\mathrm{x}\left(\frac{\mathrm{25}}{\mathrm{150}}\right)\:=\:\mathrm{1} \\ $$$$\therefore\:\:\mathrm{x}\left(\frac{\mathrm{1}}{\mathrm{6}}\right)\:=\:\mathrm{1} \\ $$$$\therefore\:\:\frac{\mathrm{x}}{\mathrm{6}}\:=\:\mathrm{1} \\ $$$$\mathrm{Cross}\:\mathrm{multiply} \\ $$$$\therefore\:\:\mathrm{x}\:=\:\mathrm{6} \\ $$$$\mathrm{Hence}\:\mathrm{it}\:\mathrm{will}\:\mathrm{take}\:\mathrm{both}\:\mathrm{of}\:\mathrm{them}\:\mathrm{6}\:\mathrm{days}\:\mathrm{to}\: \\ $$$$\mathrm{finish}\:\mathrm{the}\:\mathrm{work}\:\mathrm{if}\:\mathrm{they}\:\mathrm{both}\:\mathrm{work}\:\mathrm{together}. \\ $$$$\mathrm{DONE}\:! \\ $$
Commented by mrW last updated on 22/Nov/16
The solution can be generalized as following:
$$\mathrm{The}\:\mathrm{solution}\:\mathrm{can}\:\mathrm{be}\:\mathrm{generalized} \\ $$$$\mathrm{as}\:\mathrm{following}: \\ $$
Commented by mrW last updated on 22/Nov/16
Commented by sandy_suhendra last updated on 22/Nov/16
it can be solved by this way : in 1 day A can do = (1/(10)) part of work in 1 day B can do = (1/(15)) part of work in 1 day A and B can do = (1/(10))+(1/(15))=(1/6) part of work so A and B can do the work in 6 days
$$\mathrm{it}\:\mathrm{can}\:\mathrm{be}\:\mathrm{solved}\:\mathrm{by}\:\mathrm{this}\:\mathrm{way}\:: \\ $$$$\mathrm{in}\:\mathrm{1}\:\mathrm{day}\:\mathrm{A}\:\mathrm{can}\:\mathrm{do}\:=\:\frac{\mathrm{1}}{\mathrm{10}}\:\mathrm{part}\:\mathrm{of}\:\mathrm{work} \\ $$$$\mathrm{in}\:\mathrm{1}\:\mathrm{day}\:\mathrm{B}\:\mathrm{can}\:\mathrm{do}\:=\:\frac{\mathrm{1}}{\mathrm{15}}\:\mathrm{part}\:\mathrm{of}\:\mathrm{work} \\ $$$$\mathrm{in}\:\mathrm{1}\:\mathrm{day}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{can}\:\mathrm{do}\:=\:\frac{\mathrm{1}}{\mathrm{10}}+\frac{\mathrm{1}}{\mathrm{15}}=\frac{\mathrm{1}}{\mathrm{6}}\:\mathrm{part}\:\mathrm{of}\:\mathrm{work} \\ $$$$\mathrm{so}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{can}\:\mathrm{do}\:\mathrm{the}\:\mathrm{work}\:\mathrm{in}\:\mathrm{6}\:\mathrm{days} \\ $$

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