Elementary arithmetic, with brief notices of its history... by Robert Potts.

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2. Since the work of 5 men is equivalent to that of 7 women, the work of I
woman is denoted by -' that of a man; and the work of 7 men and 5 women will be
Idenoted by -7- work of a man. The number of days is 34 I.
3. The work of two men is equivalent to that of 3 boys, and the work of 9 boys
will be equal to that of 6 men, and therefore the work of 12 men and 9 boys will be
the same as that of 18 men. 1 man can perform,5 of the work in 1 day, and the
work of a boy as 2 of thaof tt f a man, or g7 in 1 day. Hence the work of 1 man and
1 boy in 1 day is denoted by Th. The number of days is 30.
4. 30-.o days. 5. 28 days. 6. A man in 11 days, a woman in 33 days, and a
boy in 38-l- days. 7. A man in 31l~ days, and a boy in 252 days. 8. 360 days.
9. 4 days.
XXX.
1. If the work be denoted by 1. Then A and B do 1 in 20 days, or -L in 1 day.
B does 1 in 50 days, or -I in 1 day. Hence A does -— = loo in one day, and
]. =1o= 3 = 33 days in which A could finish the work by himself.
And A does 1 in 1 day, or in 20 clays he does 0 or - of the work.
50 50 5
3 3X20 03
B does —,, or
100 100 5
2. A does 1 in 11 days, therefore Y in 1 day. B does 1 in 17 days, therefore
-- in I day.
Then~!+ — And 1+ - -'= =68- dcays.
4 I T Y 7 I87 2
Together they complete the work in 6 1 days.
3. A and B do 1 in 6 days, and I in 1 day. B does - in 11 days, and - in 1
dlay. And A does T-5=-: and 1 3- -30 days, 1-2=- -=7.
That is, A does the work in 30 days, and B in 7~ days.
4. A and B do 1 in 12 days, and c- in 1 day; similarly A and C do - in 1 day,
andl B and C -D in 1 day.
Then -121 1 or is double of what A, B, C do in 1 day,
12 15 20 5
and therefore A, B, C do of the work in 1 day, 1- = 10 days,
10 10
or, together, they finish the work in 10 days.
Again _l 6 -5- what C does in i day.
" 10 12 60 60
1 1 3-2 1
1 1 8=3 20 1- what B does in 1 day.
10 15 30 30
1 1 2 —1 1,what A does in 1 day.
10 20 20 20
And A, B, C, separately, do the work in 20, 30, and 60 days respectively.
5. A does 1 in 15 days, and -5 in 1 day. B does 1 in 18 days and -L in 1 day... and B together in 3 days do 1 - or 1 of the work.
5 6 30
and 1 - - = of work remains to be done.
30 30
HIere B leaves, A continues, and is joined by C, who together finish the part
left 19 in 4 days. Of this A does 4 in 4 days.
30 15
And 19 4 11 work left.
30 15 30
C does in 4 days, or 11 in 1 day, 1 1=12_ 10- cldays.
30 120 120 11 1
That is, C could do the work by himself in 10-lO days.
6. 100 dcays. 7. 1 hrs. 8. 414 days, 420 days, 5.2 days. 9. 2 days. 10. 23 brsa
3. iy7.rs.u 8. 4 4.