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2 women A and B can mow a field in 8 an 12 hrs resp. They

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remgeo
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2 women A and B can mow a field in 8 an 12 hrs resp. They [#permalink] New post   04 May 2006, 08:31
2 women A and B can mow a field in 8 an 12 hrs resp. They work for an hr alternately, A beginning at 9 am. When will the work be completed?



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Re: 2 women A and B can mow a field in 8 an 12 hrs resp. They [#permalink] New post   04 May 2006, 08:36
18:30 or 6:30pm???
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Re: 2 women A and B can mow a field in 8 an 12 hrs resp. They [#permalink] New post   04 May 2006, 08:38
the work will be finished in total 9 hrs 30 min

so from 9 a.m add 9 hrs 30 min it will come to 18 :30 hrs or 6:30 P.M

in 2 hours they work 1/8 +1/12 of the work i,.e = 5/24 of the work
in 8 hrs they will finish 20/24 of the work . 4/24 of the work will be left that A can do in 1/8 of the work in 1 hour so 1/24 of the work will be left that B can do in 30 min so total 9 hr 30 m


I hope i didnt make any silly mistake .
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Re: 2 women A and B can mow a field in 8 an 12 hrs resp. They [#permalink] New post   04 May 2006, 10:00
6.30 pm
draw a scheme

3/24 5/24 8/24 10/24 and so on
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Re: 2 women A and B can mow a field in 8 an 12 hrs resp. They [#permalink] New post   Updated on: 04 May 2006, 18:36
both can do 5/24th part of work in 1 hr

So each working for 4 hours 20/24 is done = 5/6 part of work in 8 hrs

9th hour A takes up and complete 1/8 work so 1/24 work is left

But B takes 1/2 hour to clte it 'cos it can complete 1/12 in 1 hour

So 9 and half hours ...which is 6:30PM

Originally posted by trivikram on 04 May 2006, 18:12.
Last edited by trivikram on 04 May 2006, 18:36, edited 2 times in total.
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Re: 2 women A and B can mow a field in 8 an 12 hrs resp. They [#permalink] New post   04 May 2006, 18:24
Brute force it.

A can mow 1/8 of the field in 1 hour
B can mow 1/12 of the field in 1 hour

A starts work first --> Left 7/8 of the job
B starts work next ---> 19/24 left
A --------------------> 2/3
B --------------------> 7/12
A --------------------> 11/24
B --------------------> 3/8
A --------------------> 7/24
B --------------------> 5/24
A --------------------> 1/12
B --------------------> 0

So work ends at 7pm.
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Re: 2 women A and B can mow a field in 8 an 12 hrs resp. They [#permalink] New post   04 May 2006, 20:26
remgeo wrote:
2 women A and B can mow a field in 8 an 12 hrs resp. They work for an hr alternately, A beginning at 9 am. When will the work be completed?

a can work 1/8 of work in 1 hour
b can work 1/12 of work in 1 hour
a+b can work (1/8 + 1/12) = 5/24 in 2 hours.
a+b can work (1/8 + 1/12 + 1/8 + 1/12 + 1/8 + 1/12 + 1/8 + 1/12 + 1/8) = in 9 hours.

now there remains 1-23/24 = 1/24 works and its B's turn.

if b can finish 1/2 in 1 hour, then he/she can finish 1/2 of 1/12 = 1/24 in 1/2 hour.

total hours taken is 9 hours 30 minuets. so the time is 6.30 when the job is completed.....
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Re: 2 women A and B can mow a field in 8 an 12 hrs resp. They [#permalink] New post   05 May 2006, 01:27
ywilfred wrote:
Brute force it.

A can mow 1/8 of the field in 1 hour
B can mow 1/12 of the field in 1 hour

A starts work first --> Left 7/8 of the job
B starts work next ---> 19/24 left
A --------------------> 2/3
B --------------------> 7/12
A --------------------> 11/24
B --------------------> 3/8
A --------------------> 7/24
B --------------------> 5/24
A --------------------> 1/12
B --------------------> 0

So work ends at 7pm.

A beginning at 9 am
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shevy
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Re: 2 women A and B can mow a field in 8 an 12 hrs resp. They [#permalink] New post   07 May 2006, 14:45
Good problem...finishes at 6.30



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Re: 2 women A and B can mow a field in 8 an 12 hrs resp. They [#permalink]
07 May 2006, 14:45
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