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It takes 4 hours for two pipes to simultaneously fill up a swimming pool. If one pipe at a time is used to fill up the swimming pool, the smaller pipe would take 6 hours longer than the larger pipe. Find the time it would take the lager pipe to fill up the swimming pool.
中四數學題目
2008-10-07 6:51 am
回答 (2)
2008-10-07 7:15 am
large pipe x hr,and the small pipe (x+6) hr
then
1/(1/x+1/x+6)=4
solve that
x=6,
it takes 6 hr
then
1/(1/x+1/x+6)=4
solve that
x=6,
it takes 6 hr
2008-10-07 7:13 am
Let the time for the large pipe to fill up the swimming pool be x hr and the time for the smaller pipe to fill up the swimming pool be x+6 hr
Let v be the volume of the swimming pool to be filled
The volume of swimming pool to fill water in one hour
v/4 = v/x + v/(x+6)
x(x+6) = 4(x+6) + 4x
x^2 + 6x = 8x+24
x^2 - 2x - 24 = 0
(x - 6)(x+4) = 0
x = 6 hrs or -4(rejected)
Let v be the volume of the swimming pool to be filled
The volume of swimming pool to fill water in one hour
v/4 = v/x + v/(x+6)
x(x+6) = 4(x+6) + 4x
x^2 + 6x = 8x+24
x^2 - 2x - 24 = 0
(x - 6)(x+4) = 0
x = 6 hrs or -4(rejected)
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