A and B can do a job together in 80 days, B and C in 20 days.












0












$begingroup$


A does the job for 5 days, then B comes over and does it for 15 days, then C does it for 18 days and the job is finished. How much time does C need to do the job alone?



Attempt:



Let their job effeciencies be a, b and c jobs per day respectively.



Then



$a+b=frac{1}{80}$



$b+c=frac{1}{20}$



$5a+15b+18c=1$



From equation 2,



$b=frac{1}{20}-c$



From equation 1,



$a=frac{1}{80}-b=frac{1}{80}-(frac{1}{20}-c)=frac{1}{80}-frac{1}{20}+c$



Substituting $a$ and $b$ in equation 3 and solving for $c$,



$5(frac{1}{80}-frac{1}{20}+c)+15(frac{1}{20}-c)+18c=1$



I solved for c and then took its reciprocal $frac{1}{c}$ and got 18 days as answer.



However, that makes no sense because B and C do it together in 20 days. There's no way C can do it alone in 18 days. Where am I wrong?






fractions word-problem







share|cite|improve this question











$endgroup$












  • $begingroup$
    Can b do negative work in this problem? because that seems to be the value of b with your equations. $a = frac{11}{640}, b = -frac{3}{640}, c = frac{7}{128}$
    $endgroup$
    – Sik Feng Cheong
    Dec 20 '18 at 15:46












  • $begingroup$
    @SikFengCheong Are my equations incorrect then? I've written the problem in words above.
    $endgroup$
    – Ryder Rude
    Dec 20 '18 at 15:52










  • $begingroup$
    Your equations seem correct, and I get the same answer as @SikFengCheong ... I think that indeed B is doing negative work, i.e. B is hampering, rather than helping.
    $endgroup$
    – Bram28
    Dec 20 '18 at 15:54










  • $begingroup$
    @Bram28 I didn't know hampering was a thing. This problem gave me a headache. Thanks.
    $endgroup$
    – Ryder Rude
    Dec 20 '18 at 15:55








  • 2




    $begingroup$
    @RyderRude Well, suppose the job was something like stuffing envelopes ... then B is someone who is taking stuff out of envelopes .. or moves the envelopes out of the way just when A or C needs them .. or ...
    $endgroup$
    – Bram28
    Dec 20 '18 at 15:56


















0












$begingroup$


A does the job for 5 days, then B comes over and does it for 15 days, then C does it for 18 days and the job is finished. How much time does C need to do the job alone?



Attempt:



Let their job effeciencies be a, b and c jobs per day respectively.



Then



$a+b=frac{1}{80}$



$b+c=frac{1}{20}$



$5a+15b+18c=1$



From equation 2,



$b=frac{1}{20}-c$



From equation 1,



$a=frac{1}{80}-b=frac{1}{80}-(frac{1}{20}-c)=frac{1}{80}-frac{1}{20}+c$



Substituting $a$ and $b$ in equation 3 and solving for $c$,



$5(frac{1}{80}-frac{1}{20}+c)+15(frac{1}{20}-c)+18c=1$



I solved for c and then took its reciprocal $frac{1}{c}$ and got 18 days as answer.



However, that makes no sense because B and C do it together in 20 days. There's no way C can do it alone in 18 days. Where am I wrong?






fractions word-problem







share|cite|improve this question











$endgroup$












  • $begingroup$
    Can b do negative work in this problem? because that seems to be the value of b with your equations. $a = frac{11}{640}, b = -frac{3}{640}, c = frac{7}{128}$
    $endgroup$
    – Sik Feng Cheong
    Dec 20 '18 at 15:46












  • $begingroup$
    @SikFengCheong Are my equations incorrect then? I've written the problem in words above.
    $endgroup$
    – Ryder Rude
    Dec 20 '18 at 15:52










  • $begingroup$
    Your equations seem correct, and I get the same answer as @SikFengCheong ... I think that indeed B is doing negative work, i.e. B is hampering, rather than helping.
    $endgroup$
    – Bram28
    Dec 20 '18 at 15:54










  • $begingroup$
    @Bram28 I didn't know hampering was a thing. This problem gave me a headache. Thanks.
    $endgroup$
    – Ryder Rude
    Dec 20 '18 at 15:55








  • 2




    $begingroup$
    @RyderRude Well, suppose the job was something like stuffing envelopes ... then B is someone who is taking stuff out of envelopes .. or moves the envelopes out of the way just when A or C needs them .. or ...
    $endgroup$
    – Bram28
    Dec 20 '18 at 15:56
















0












0








0





$begingroup$


A does the job for 5 days, then B comes over and does it for 15 days, then C does it for 18 days and the job is finished. How much time does C need to do the job alone?



Attempt:



Let their job effeciencies be a, b and c jobs per day respectively.



Then



$a+b=frac{1}{80}$



$b+c=frac{1}{20}$



$5a+15b+18c=1$



From equation 2,



$b=frac{1}{20}-c$



From equation 1,



$a=frac{1}{80}-b=frac{1}{80}-(frac{1}{20}-c)=frac{1}{80}-frac{1}{20}+c$



Substituting $a$ and $b$ in equation 3 and solving for $c$,



$5(frac{1}{80}-frac{1}{20}+c)+15(frac{1}{20}-c)+18c=1$



I solved for c and then took its reciprocal $frac{1}{c}$ and got 18 days as answer.



However, that makes no sense because B and C do it together in 20 days. There's no way C can do it alone in 18 days. Where am I wrong?






fractions word-problem







share|cite|improve this question











$endgroup$




A does the job for 5 days, then B comes over and does it for 15 days, then C does it for 18 days and the job is finished. How much time does C need to do the job alone?



Attempt:



Let their job effeciencies be a, b and c jobs per day respectively.



Then



$a+b=frac{1}{80}$



$b+c=frac{1}{20}$



$5a+15b+18c=1$



From equation 2,



$b=frac{1}{20}-c$



From equation 1,



$a=frac{1}{80}-b=frac{1}{80}-(frac{1}{20}-c)=frac{1}{80}-frac{1}{20}+c$



Substituting $a$ and $b$ in equation 3 and solving for $c$,



$5(frac{1}{80}-frac{1}{20}+c)+15(frac{1}{20}-c)+18c=1$



I solved for c and then took its reciprocal $frac{1}{c}$ and got 18 days as answer.



However, that makes no sense because B and C do it together in 20 days. There's no way C can do it alone in 18 days. Where am I wrong?






fractions word-problem




fractions word-problem






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 20 '18 at 15:41









Sik Feng Cheong

1579




1579










asked Dec 20 '18 at 15:35









Ryder RudeRyder Rude

444111




444111












  • $begingroup$
    Can b do negative work in this problem? because that seems to be the value of b with your equations. $a = frac{11}{640}, b = -frac{3}{640}, c = frac{7}{128}$
    $endgroup$
    – Sik Feng Cheong
    Dec 20 '18 at 15:46












  • $begingroup$
    @SikFengCheong Are my equations incorrect then? I've written the problem in words above.
    $endgroup$
    – Ryder Rude
    Dec 20 '18 at 15:52










  • $begingroup$
    Your equations seem correct, and I get the same answer as @SikFengCheong ... I think that indeed B is doing negative work, i.e. B is hampering, rather than helping.
    $endgroup$
    – Bram28
    Dec 20 '18 at 15:54










  • $begingroup$
    @Bram28 I didn't know hampering was a thing. This problem gave me a headache. Thanks.
    $endgroup$
    – Ryder Rude
    Dec 20 '18 at 15:55








  • 2




    $begingroup$
    @RyderRude Well, suppose the job was something like stuffing envelopes ... then B is someone who is taking stuff out of envelopes .. or moves the envelopes out of the way just when A or C needs them .. or ...
    $endgroup$
    – Bram28
    Dec 20 '18 at 15:56




















  • $begingroup$
    Can b do negative work in this problem? because that seems to be the value of b with your equations. $a = frac{11}{640}, b = -frac{3}{640}, c = frac{7}{128}$
    $endgroup$
    – Sik Feng Cheong
    Dec 20 '18 at 15:46












  • $begingroup$
    @SikFengCheong Are my equations incorrect then? I've written the problem in words above.
    $endgroup$
    – Ryder Rude
    Dec 20 '18 at 15:52










  • $begingroup$
    Your equations seem correct, and I get the same answer as @SikFengCheong ... I think that indeed B is doing negative work, i.e. B is hampering, rather than helping.
    $endgroup$
    – Bram28
    Dec 20 '18 at 15:54










  • $begingroup$
    @Bram28 I didn't know hampering was a thing. This problem gave me a headache. Thanks.
    $endgroup$
    – Ryder Rude
    Dec 20 '18 at 15:55








  • 2




    $begingroup$
    @RyderRude Well, suppose the job was something like stuffing envelopes ... then B is someone who is taking stuff out of envelopes .. or moves the envelopes out of the way just when A or C needs them .. or ...
    $endgroup$
    – Bram28
    Dec 20 '18 at 15:56


















$begingroup$
Can b do negative work in this problem? because that seems to be the value of b with your equations. $a = frac{11}{640}, b = -frac{3}{640}, c = frac{7}{128}$
$endgroup$
– Sik Feng Cheong
Dec 20 '18 at 15:46






$begingroup$
Can b do negative work in this problem? because that seems to be the value of b with your equations. $a = frac{11}{640}, b = -frac{3}{640}, c = frac{7}{128}$
$endgroup$
– Sik Feng Cheong
Dec 20 '18 at 15:46














$begingroup$
@SikFengCheong Are my equations incorrect then? I've written the problem in words above.
$endgroup$
– Ryder Rude
Dec 20 '18 at 15:52




$begingroup$
@SikFengCheong Are my equations incorrect then? I've written the problem in words above.
$endgroup$
– Ryder Rude
Dec 20 '18 at 15:52












$begingroup$
Your equations seem correct, and I get the same answer as @SikFengCheong ... I think that indeed B is doing negative work, i.e. B is hampering, rather than helping.
$endgroup$
– Bram28
Dec 20 '18 at 15:54




$begingroup$
Your equations seem correct, and I get the same answer as @SikFengCheong ... I think that indeed B is doing negative work, i.e. B is hampering, rather than helping.
$endgroup$
– Bram28
Dec 20 '18 at 15:54












$begingroup$
@Bram28 I didn't know hampering was a thing. This problem gave me a headache. Thanks.
$endgroup$
– Ryder Rude
Dec 20 '18 at 15:55






$begingroup$
@Bram28 I didn't know hampering was a thing. This problem gave me a headache. Thanks.
$endgroup$
– Ryder Rude
Dec 20 '18 at 15:55






2




2




$begingroup$
@RyderRude Well, suppose the job was something like stuffing envelopes ... then B is someone who is taking stuff out of envelopes .. or moves the envelopes out of the way just when A or C needs them .. or ...
$endgroup$
– Bram28
Dec 20 '18 at 15:56






$begingroup$
@RyderRude Well, suppose the job was something like stuffing envelopes ... then B is someone who is taking stuff out of envelopes .. or moves the envelopes out of the way just when A or C needs them .. or ...
$endgroup$
– Bram28
Dec 20 '18 at 15:56












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$begingroup$

If we also solve for $a$ and $b$ we get $frac{11}{640}$ and $-frac{3}{640}$ respectively. This means that either there is a mistake in the question or person B's incompetence hinders production! :)






share|cite|improve this answer









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    $begingroup$

    If we also solve for $a$ and $b$ we get $frac{11}{640}$ and $-frac{3}{640}$ respectively. This means that either there is a mistake in the question or person B's incompetence hinders production! :)






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      If we also solve for $a$ and $b$ we get $frac{11}{640}$ and $-frac{3}{640}$ respectively. This means that either there is a mistake in the question or person B's incompetence hinders production! :)






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        If we also solve for $a$ and $b$ we get $frac{11}{640}$ and $-frac{3}{640}$ respectively. This means that either there is a mistake in the question or person B's incompetence hinders production! :)






        share|cite|improve this answer









        $endgroup$



        If we also solve for $a$ and $b$ we get $frac{11}{640}$ and $-frac{3}{640}$ respectively. This means that either there is a mistake in the question or person B's incompetence hinders production! :)







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 20 '18 at 15:59









        Richard AmblerRichard Ambler

        1,308515




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