SOLUTION: Q1. if 2 men or 3 women or 6boys can do a piece o work in 70 days,in what time would 2 men, 6 women and 24 boys to do it? Q2.30 men can do a job in 25 days when should 12 men ca

Question 611925: Q1. if 2 men or 3 women or 6boys can do a piece o work in 70 days,in what time would 2 men, 6 women and 24 boys to do it?
Q2.30 men can do a job in 25 days when should 12 men can leave the work,if the whole is to be done in 35 days after they leave the work?
Q3.A and B can do a job together in 15 days. whereas A alone can do it in 21 days. if B does the work for only half a day, how long shall it take to do the job now by A and B?
Found 2 solutions by ankor@dixie-net.com, vvnrichards:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Q1. If 2 men or 3 women or 6 boys can do a piece of work in 70 days,
:
2*70 = 140 man-days to finish the job
therefore 140 days for one man to do the job
:
3*70 = 210 girl-days to finish the job
therefore. 210 days required for 1 girl to do the job
:
6*70 = 420 boy-days to do the job
therefore: 420 days for 1 boy to do the job
:
"in what time would 2 men, 6 women and 24 boys to do it?
:
Let t = time required by this scenario
Let the completed job = 1
+ + = 1
Reduce the fractions
+ + = 1
Multiply by 70 to clear the denominators, results
t + 2t + 4t = 70
7t = 70
t = 10 days for this crew to do the job
:
:
Q2.30 men can do a job in 25 days
30 * 25 = 750 man-days required to do the job
:
"when should 12 men can leave the work, if the whole is to be done in 35 days after they leave the work?
18 men work the whole 35 days
let d = no. of days worked the 12 who leave
35*18 + 12d = 750
630 + 12d = 750
12d = 750 - 630
12d = 120
d = 10 days, the 12 men can leave
:
:
Q3. A and B can do a job together in 15 days. whereas A alone can do it in 21 days. :
Find how long it would take B to do the job alone (b)
+ = 1
multiply by 21b, results:
15b + 15(21) = 21b
315 = 21b - 15b
315 = 6b
b =
b = 52.5 days, B alone
:
" If B does the work for only half a day, how long shall it take to do the job now by A and B?"
+ = 1
convert the 2nd fraction to a decimal
+ .0095238 = 1
= 1 - .0095238
= .990476
t = .990476 * 21
t = 20.8 days

Answer by vvnrichards(3) (Show Source): You can put this solution on YOUR website!
Q1. If 2 men or 3 women or 6 boys can do a piece of work in 70 days,
:
2*70 = 140 man-days to finish the job
therefore 140 days for one man to do the job
:
3*70 = 210 girl-days to finish the job
therefore. 210 days required for 1 girl to do the job
:
6*70 = 420 boy-days to do the job
therefore: 420 days for 1 boy to do the job
:
"in what time would 2 men, 6 women and 24 boys to do it?
:
Let t = time required by this scenario
Let the completed job = 1
+ + = 1
Reduce the fractions
+ + = 1
Multiply by 70 to clear the denominators, results
t + 2t + 4t = 70
7t = 70
t = 10 days for this crew to do the job
:
:
Q2.30 men can do a job in 25 days
30 * 25 = 750 man-days required to do the job
:
"when should 12 men can leave the work, if the whole is to be done in 35 days after they leave the work?
18 men work the whole 35 days
let d = no. of days worked the 12 who leave
35*18 + 12d = 750
630 + 12d = 750
12d = 750 - 630
12d = 120
d = 10 days, the 12 men can leave
:
:
Q3. A and B can do a job together in 15 days. whereas A alone can do it in 21 days. :
Find how long it would take B to do the job alone (b)
+ = 1
multiply by 21b, results:
15b + 15(21) = 21b
315 = 21b - 15b
315 = 6b
b =
b = 52.5 days, B alone
:
" If B does the work for only half a day, how long shall it take to do the job now by A and B?"
Since B is only working for half a day, his rate will be halved.
+ =
convert the 1st and 2nd fraction to a decimal
d = 17.5 days
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