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14 Aug 2022, 05:40
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Difficulty:
45%
(medium)
Question Stats:
72% (02:17) correct
28%
(02:39)
wrong
based on 269
sessions
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There are many taps in the pool. One tap can fill the pool in 50 hours. Someone opens the first tap and further opens a new tap each following hour. In approximately how many hours the pool will be filled?
(A) 6
(B) 8
(C) 9
(D) 10
(E) 12
(A) 6
(B) 8
(C) 9
(D) 10
(E) 12
14 Aug 2022, 06:40
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The first tap will be open for T hours, the time we're looking for.
Each succeeding tap will be open for one hour less than the prior tap, until the final tap is open for just 1 hour.
This looks like:
1 = T/50 + (T-1)/50 +
(T-2)/50 + ...1/50
So going backwards, the numerator looks like:
1+2+3+...T, so
1 = (1/50)(1+2+3...T), or
50 = (1+2+3+...T)
A formula for the right is:
n(n+1)/2 = T(T+1)/2, so:
50=T(T+1)/2 and:
T^2+T-100=0
Using quadratic formula:
T= (-1+(1+400)^.5)/2, which ignoring the 1 added to 400:
(-1+20)/2 = 9.5 = approximately
10
Posted from my mobile device
Each succeeding tap will be open for one hour less than the prior tap, until the final tap is open for just 1 hour.
This looks like:
1 = T/50 + (T-1)/50 +
(T-2)/50 + ...1/50
So going backwards, the numerator looks like:
1+2+3+...T, so
1 = (1/50)(1+2+3...T), or
50 = (1+2+3+...T)
A formula for the right is:
n(n+1)/2 = T(T+1)/2, so:
50=T(T+1)/2 and:
T^2+T-100=0
Using quadratic formula:
T= (-1+(1+400)^.5)/2, which ignoring the 1 added to 400:
(-1+20)/2 = 9.5 = approximately
10
Posted from my mobile device
28 Sep 2023, 03:30
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Bad question - rounding up to 10 means that they pool would overflow.
