Question 462476
Let {{{ c }}} = speed of current
Let {{{ t }}} = time to go either upstream or downstream
given:
Speed in still water = {{{ 63 }}} mi/hr
Going upstream, speed = {{{ 63 - c }}}
Going downstream, speed = {{{ 63 + c }}}
Upstream:
(1) {{{ 120 = (63 - c)*t }}}
Downstream:
(2) {{{ 150 = (63 + c)*t }}}
Add the equations
{{{ 120 + 150 = (63-c)*t + (63+c)*t }}}
{{{ 270 = 63t - c*t + 63t + c*t }}}
{{{ 270 = 126t }}}
{{{ t = 2.143 }}} hrs
Substitute in (2)
(2) {{{ 150 = (63 + c)*2.143 }}}
(2) {{{ 150 = 135 + 2.143c }}}
(2) {{{ 2.143c = 15 }}}
(2) {{{ c = 7 }}}
The speed of the current is 7 mi/hr
check:
(1) {{{ 120 = (63 - 7)*2.143 }}}
(1) {{{ 120 = 56*2.143 }}}
(1) {{{ 120 = 120.008 }}} (rounding off error)
OK