Can someone help me solve this question?
Mary takes 6 days to sew a blanket. Jane takes 10 days to sew a similar blanket. How long would they take if they are to sew a blanket together? Express your answer in a fraction in its simplest form.
Mary sews 1/6 of the blanket in 1 day
Jane sews 1/10 of the blanket in 1 day
Together, they sew 1/6 + 1/10 = 8/30 in 1 day.
1 / 8/30 = 3 3/4 days
o if i not wrong this question type is called inverse dunno wat de..
i was very lousy at this but later i learnt it this way.. and it is very effective to me..
how i learnt is was always writing down the info first, for example in ur case :
1 blanket
mary -----> 6 days
jane -------> 10 days
so later u think, in 1 day, how many blanket can she sew?
1 blanket ------> 6 days
1 day ----------> refer to below
so now u think, mary take 6 day to sew one bloody blanket, then one day, she sew more blanket than the 6 day? or less blanket than 6 days? think think think...
later u think, o! mary 6 day sew 1 blanket, meaning 1 day she can sew a bit only.. so is lesser than 1 blanket le..
so mary, 1 day -------> 1 divided by (a number) of blanket
now u think again, the number would be wat? the number must be related to mary, related to the number of day right? so now u think and think, o the number can only be 6 days!
so mary, 1 day -------> 1 divided by 6 of blanket!
now do the same thing for Jane.
mary, 1 day -----> 1/6 blanket
jane, 1 day -------> 1/10 blanket
now time for a simple check if u are right so far, using ur common sense, would a person take 10 days to sew a blanket, sew more blanket than a person who take only 6 days to sew a blanket?
so jane take so long to sew a blanket (10 days), obviously sew lesser blanket in a day than mary who take only 6 days to sew a blanket
ok so now u check, all u had done so far is correct
so now the question ask u, they sew together, how long they take to sew a dam blanket?
now u think and think,
mary -------> 6 days
jane ----------> 10 days
both do together ----------> faster than one person or slower?
of course is faster! now in ur heart, u must visualize that the answer is lesser than 6.
now, calculate the amount of blanket they can sew in a day,
mary + jane ------> how many blanket?
now u think, mary and jane dun care each other, they sew their own thing, then end of that day they combine their blanket, meaning that the sewing together doesnt affects the speed, they each have their own speed.
so mary + jane ----------> 1/10 + 1/6 = 4/15
now check again, is 4/15 more than 1/6? if not, try other numbers and way.. make sure it makes sense. if yes, and it makes sense (use ur common sense), then good le! u are on the right track!
now the question ask u how long, not how much blanket, since they cannot even finish a blanket in a day, they must have took more than a day to finish sewing this blanket, now think back, ur answer must be lower than 6 but higher than 1... this is to check and confirm ur answer...
now do ur working,
1 day -------> 4/15
1 blanket ------> refer again
now i also confuse already, but nvm i got my common sense, now u got 2 numbers to work with, "1" and "4/15", now how u gonna work them out in order for them to be bigger than 1 and lower than 6, ( please note that addition (+) and subtracting (-) do not work in this step, so only left with dividing or multiplying.. but multiplying 4/15 and 1 is lower than 1 itself.. so u divide 4/15 by 1, the answer is still lower than 1, so u try again 1 divided by 4/15, ok this time u get an answer bigger than 1 lower than 6... congratz
then write ur working,
1 day --------> 4/15 of blanket
1 full blanket ---------> 1 divided by 4/15 = 3.75 day (remember to change ur answer to fraction, cuz the question ask u to)
therefore, they both need 3 3/4 day to finish sewing one bloody blanket.
btw, if i am wrong or have any misconceptions, please please please tell me, i learnt this not long ago by myself, i do not want to have any misconception on this as i am having my "o" levels in the next few months!
if u wan to summarize it, the method for doing this type of question is common sense, numbers u are working with must be related, use ur common sense!
IA
It is common sense in a way but at O's this should be instant usage of algebra. I hope you can do this question quicker than that now cos you will never finish the exam in time if you need take this long to get your answer.
TS is a tutor not a P6 student.
o haha sorry! i tot TS is a student...
cuz early this yr i was still confused on this type of question... then later someone told me this, and i can really remember it well because of this...
so i thought it would be good to share this to other ppl reading too... yeap the more u do this type of question the quicker u would answer... this is maths ma haha!
just my way of learning ba... no need to follow if dun like my style...
and dkcx, thanks and no need worry haha... i can finish on time, just that some dunno how to do haha! trying hard and thanks!
IA
I get it now. Thanks to everyone who contributed! :)