Probability played a role in the rigging of the April 24, 1980, Pennsylvania state lottery. To determine each digit of the three
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L = rate of the large hose
S = rate of the small hose
we know the sum of their rates deliver the swimming pool filled up in 35 minutes, thus L + S = 35.
now, the large hose can do it in 60 minutes, that means that in 1 minute, the large hose has only done 1/60 th of the work.
the small hose can do the whole thing in S minutes, that means in 1 minute it has only done 1/S th of the whole work.
and since both of them working together can do it in 35 minutes, then in 1 minute they both have done 1/35 th of the whole job.