Question

A and B can do a job in 6 days, B and C in 9 days, and A and C in 12 days. How much time will they take to complete the job if they all work together? How long will each of them take to do the job?​

Answer 1

Step-by-step explanation:

A+B=6. 6

B+C=9. 36. 4

A+C=12. 3

2(A+B+C)= 36/13

A+B+C=18/13DAYS

Answer 2

Answer:

$\\ 5 \times \frac{7}{13} \\a = 14 \times \frac{2}{5} \\b = 10 \times \frac{2}{7} \\ c = 72$

Step-by-step explanation:

ᗩ ᴀɴᴅ ᗷ ᴄᴀɴ ᴅᴏ ᴛʜᴇ ᴊᴏʙ ɪɴ 6 ᴅᴀʏs

.•. ɪɴ 1 ᴅᴀʏ ᗩ ᴀɴᴅ ᗷ ᴄᴀɴ ᴅᴏ ᴛʜᴇ ᴊᴏʙ =

$\frac{1}{6}$

☞︎︎︎

$|1|$

ᗷ ᴀɴᴅ ᑕ ᴄᴀɴ ᴅᴏ ᴛʜᴇ ᴊᴏʙ ɪɴ 9 ᴅᴀʏs

.•. ɪɴ 1 ᴅᴀʏ ᗷ ᴀɴᴅ ᑕ ᴄᴀɴ ᴅᴏ ᴛʜᴇ ᴊᴏʙ =

$\frac{1}{9}$

☞︎︎︎

$|2|$

ᗩ ᴀɴᴅ ᑕ ᴄᴀɴ ᴅᴏ ᴛʜᴇ ᴊᴏʙ ɪɴ 12 ᴅᴀʏs

.•. ɪɴ 1 ᴅᴀʏ ᗩ ᴀɴᴅ ᑕ ᴄᴀɴ ᴅᴏ ᴛʜᴇ ᴊᴏʙ =

$\frac{1}{12}$

☞︎︎︎

$|3|$

ᴀᴅᴅɪɴɢ ᴀʟʟ ᴇǫᴜᴀᴛɪᴏɴs

$|1| and |2| and |3|$

.

ɪɴ 1 ᴅᴀʏ , ( ᴡᴏʀᴋ ᴅᴏɴᴇ ʙʏ 2ᗩ , 2ᗷ ᴀɴᴅ 2ᑕ )

$= \frac{1}{6} + \frac{1}{9} + \frac{1}{12} \\ = \frac{13}{36}$

.•.2 ( ᴡᴏʀᴋ ᴅᴏɴᴇ ʙʏ ᴀ , ʙ , ᴄ ɪɴ 1 ᴅᴀʏ )

$\frac{13}{36} .$

.•.( ᴡᴏʀᴋ ᴅᴏɴᴇ ʙʏ ᴀ , ʙ , ᴄ ɪɴ 1 ᴅᴀʏ )

$\frac{13}{36} \div 2 = \frac{13}{72}$

☞︎︎︎

$|4|$

ʜᴇɴᴄᴇ , ᴀ , ʙ , ᴄ ᴛᴏɢᴇᴛʜᴇʀ ᴄᴀɴ ᴄᴏᴍᴘʟᴇᴛᴇ ᴊᴏʙ ɪɴ 1 ᴅᴀʏ

$1 \: day \div \frac{13}{72} = \frac{72}{13} days \: = 5 \times \frac{7}{13} days.$

sᴜʙsᴛʀᴀᴄᴛɪɴɢ ( 4 ) ғʀᴏᴍ ( 1 ) = ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ᴛᴏ ᴅᴏ ᴛʜᴇ ᴊᴏʙ ʙʏ 'ᴄ' ɪs

$\frac{13}{72} - \frac{1}{6} \\ \\ = \frac{13 - 12}{72} \\ \\ = \frac{1}{72}$

.•. 'ᴄ' ᴄᴀɴ ᴅᴏ ᴛʜᴇ ᴊᴏʙ ɪɴ

$72days$

sᴜʙsᴛʀᴀᴄᴛɪɴɢ ( 4 ) ғʀᴏᴍ ( 2 ) = ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ᴛᴏ ᴅᴏ ᴛʜᴇ ᴊᴏʙ ʙʏ 'ʙ' ɪs

$\frac{13}{72} - \frac{1}{9} \\ \\ = \frac{13 - 8}{72} \\ \\ = \frac{5}{72}$

.•. 'ʙ' ᴄᴀɴ ᴅᴏ ᴛʜᴇ ᴊᴏʙ ɪɴ

$\frac{72}{5} days \\ \\ = 10 \times \frac{2}{7}$

sᴜʙsᴛʀᴀᴄᴛɪɴɢ ( 4 ) ғʀᴏᴍ ( 3 ) = ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ᴛᴏ ᴅᴏ ᴛʜᴇ ᴊᴏʙ ʙʏ 'ᴀ' ɪs

$\frac{13}{72} - \frac{1}{12} \\ \\ \frac{13 - 6}{72} \\ \\ = \frac{7}{72}$

.•. 'ᴀ' ᴄᴀɴ ᴅᴏ ᴛʜᴇ ᴊᴏʙ ɪɴ

$\frac{72}{7} days \\ \\ = 14 \times \frac{2}{5} \: days$

$hope \: it \: helps \:$