Question 1057562
Let {{{ c }}} = the speed of the current
{{{ 59 - c }}} = speed of the boat going against the current
{{{ 59 + c }}} = speed of the boat going with the current
Let {{{ t }}} = time in hrs going both with and against the current
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Going against the current:
(1) {{{ 106 = ( 59 - c )*t }}}
Going with the current:
(2) {{{ 130 = ( 59 + c )*t }}}
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(1) {{{ t = 106 / ( 59 - c ) }}}
Plug this result into (2)
(2) {{{ 130 = ( 59 + c )*( 106 / ( 59 - c )) }}}
(2) {{{ 130*( 59 - c ) = 106*( 59 + c ) }}}
(2) {{{ 7670 - 130c = 6254 + 106c }}}
(2) {{{ 236c = 1416 }}}
(2) {{{ c = 6 }}}
The speed of the current is 6 mi/hr
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check:
(1) {{{ t = 106 / ( 59 - c ) }}}
(1) {{{ t = 106 / ( 59 - 6 ) }}}
(1) {{{ t = 106/53 }}}
(1) {{{ t = 2 }}} hrs
and
{{{ t = 130 / ( 59 + c ) }}}
{{{ t = 130 / ( 59 + 6 ) }}}
{{{ t = 130 / 65 }}}
{{{ t = 2 }}} hrs
OK