Question 1055877
Add the rates of filling
For the cold water faucet:
rate of filling = [ 1 bathtub filled ] / [ 5 min ]
For the hot water faucet:
rate of filling = [ 1 bathtub filled ] / [ 20 min ]
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Let {{{ t }}} = time in minutes to fill tub with both
faucets open
{{{ 1/5 + 1/20 = 1/t }}}
Multiply both sides by {{{ 20t }}}
{{{ 4t + t = 20 }}}
{{{ 5t = 20 }}}
{{{ t = 4 }}}
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With both faucets open the tub is filled in 4 min
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check:
{{{ 4/20 + 1/20 = 1/t }}}
{{{ 4/20 + 1/20 = 1/4 }}}
{{{ 5/20 = 5/20 }}}
OK