Question 809730
Let {{{ a }}} = liters of 20% solution needed
Let {{{ b }}} = liters of 70% solution needed
(1) {{{ a + b = 50 }}}
(2) {{{ ( .2a + .7b ) / 50 = .4 }}}
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(2) {{{ .2a + .7b = .4*50 }}}
(2) {{{ .2a + .7b = 20 }}}
(2) {{{ 2a + 7b = 200 }}}
Multiply both sides of (1) by {{{2}}}
and subtract (1) from (2)
(2) {{{ 2a + 7b = 200 }}}
(1) {{{ -2a -2b = -100 }}}
{{{ 5b = 100 }}}
{{{ b = 20 }}}
and, since
(1) {{{ a + b = 50 }}}
(1) {{{ a = 30 }}}
30 liters of 20% solution are needed
20 liters of 70% solution are needed
check:
(2) {{{ ( .2*30 + .7*20 ) / 50 = .4 }}}
(2) {{{ ( 6 + 14 ) / 50 = .4 }}}
(2) {{{ 20 = .4*50 }}}
(2) {{{ 20 = 20 }}}
OK
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(a) is the answer
{{{ d = r*t }}}
Subtract the rate of the current from the rate of the boat
in still water when going against the current
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Add the 2 rates when going with the current