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Sumysumy
19.10.2019 •
Social Studies
What were duties and powers of popes during the middle ages?
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Ответ:
Ответ:
Let x and y be the unit rates at which one large pump and one small pump works, respectively.
Two large/one small operate at a unit rate of
(1 pool)/(4 hours) = 0.25 pool/hour
so that
2x + y = 0.25
One large/three small operate at the same rate,
(1 pool)/(4 hours) = 0.25 pool/hour
x + 3y = 0.25
Solve for x and y. We have
y = 0.25 - 2x ==> x + 3 (0.25 - 2x) = 0.25
==> x + 0.75 - 6x = 0.25
==> 5x = 0.5
==> x = 0.1
==> y = 0.25 - 2 (0.1) = 0.25 - 0.2 = 0.05
In other words, one large pump alone can fill a 1/10 of a pool in one hour, while one small pump alone can fill 1/20 of a pool in one hour.
Now, if you have four each of the large and small pumps, they will work at a rate of
4x + 4y = 4 (0.1) + 4 (0.05) = 0.6
meaning they can fill 3/5 of a pool in one hour. If it takes time t to fill one pool, we have
(3/5 pool/hour) (t hours) = 1 pool
==> t = (1 pool) / (3/5 pool/hour) = 5/3 hours
So it would take 5/3 hours, or 100 minutes, for this arrangement of pumps to fill one pool.