Question 1041335
Rate of filling with hot water tap:
[ 1 bucket filled ] / [ 3 min ]
Rate of filling with cold water tap:
[ 1 bucket filled ] / [ 70/60 min ]
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Add the 2 rates of filling to get the rate
with both taps open
Rate with both taps open:
[ 1 bucket filled ] / [ t min ]
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{{{ 1/3 + 1/(7/6) = 1/t }}}
{{{ 1/3 + 6/7 = 1/t }}}
Multiply both sides by {{{ 21t }}}
{{{ 7t + 18t = 21 }}}
{{{ 25t = 21 }}}
{{{ t = 21/25 }}} min
{{{ ( 21/25 )*60 = 50.4 }}} sec
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the bucket is filled in 50.4 sec 
with both taps open
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check:
{{{ 1/3 + 1/(7/6) = 1/t }}}
{{{ 1/3 + 1/(7/6) = 1/.84 }}}
{{{ .333 + .8571 = 1.1905 }}}
{{{ 1.1904 = 1.1905 }}}
error due to rounding off