20 men can do a piece of work in 24 days. After working for 6 days, an additional number of men are taken to finish the work in 21 days from the beginning. Find the number of additional men .
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I tried using variation method but it didn;t work.. :(
Maths problem help please?
2015-10-21 7:43 am
回答 (2)
2015-10-21 4:14 pm
After 6 days (1/4)w was done leaving (3/4)w to do (21-6)days =15 days.
(20m)(24d) = 480 md are needed to do w. Then (3/4)(480)md are needed to do (3/4)w, ie., 360md are needed to finish the job in 15 days.
360md/15d = (360/15)m = (72/3)m = 24m are needed to finish work in 15 days, ie., 4 more men are taken on to finish the work in 15 days.
(20m)(24d) = 480 md are needed to do w. Then (3/4)(480)md are needed to do (3/4)w, ie., 360md are needed to finish the job in 15 days.
360md/15d = (360/15)m = (72/3)m = 24m are needed to finish work in 15 days, ie., 4 more men are taken on to finish the work in 15 days.
2015-10-21 8:48 am
The total work package is (20 man)*(24 days) = 480 man·days. Let m be the number of men added.
The total number of man·days is assumed to remain unchanged, so you have
.. 480 = 20*6 + (20+m)*(21-6) ... man·days during the first 6 days + man·days during the last 15 days add up to be the total job.
.. 480 = 420 + 15m ... simplify
.. 60 = 15m ... subtract 420
.. 60/15 = 4 = m ... divide by 15
The number of men added after 6 days is 4.
The total number of man·days is assumed to remain unchanged, so you have
.. 480 = 20*6 + (20+m)*(21-6) ... man·days during the first 6 days + man·days during the last 15 days add up to be the total job.
.. 480 = 420 + 15m ... simplify
.. 60 = 15m ... subtract 420
.. 60/15 = 4 = m ... divide by 15
The number of men added after 6 days is 4.
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