Question 838436
Let {{{ s }}} = Eric's speed on a bike with no wind in mi/hr
Let {{{ w }}} = the speed of the wind in mi/hr
------------------------------------
Equation riding with the wind:
(1) {{{ 162 = ( s + w )*6 }}}
Equation riding against the wind:
(2) {{{ 90 = ( s - w )*10 }}}
-----------------------
(1) {{{ 6s + 6w = 162 }}}
(1) {{{ 3s + 3w = 81 }}}
(1) {{{ s + w = 27 }}}
and
(2) {{{ 10s - 10w = 90 }}}
(2) {{{ s - w = 9 }}}
--------------------
Add the equations:
(2) {{{ s - w = 9 }}}
(1) {{{ s + w = 27 }}}
{{{ 2s = 36 }}}
{{{ s = 18 }}}
and
(2) {{{ s - w = 9 }}}
(2) {{{ 18 - w = 9 }}}
(2) {{{ w = 9 }}}
-------------------
Riding with the wind, Eric is going {{{ 18 + 9 = 27 }}} mi/hr
Riding against the wind, Eric is going {{{ 18 - 9 = 9 }}} mi/hr
The wind speed is {{{ 9 }}} mi/hr
--------------------------------
Here's a plot of (1) and (2):
{{{ w }}} is on the horizontal axis
{{{ s }}} is on the vertical axis
{{{ graph( 400, 400, -6, 30, -10, 50, x + 9, -x + 27 ) }}}
check answers:
(1) {{{ 162 = ( s + w )*6 }}}
(1) {{{ 162 = ( 18 + 9 )*6 }}}
(1) {{{ 162 = 27*6 }}}
(1) {{{ 162 = 162 }}}
-------------------------
(2) {{{ 90 = ( s - w )*10 }}}
(2) {{{ 90 = ( 18 - 9 )*10 }}}
(2) {{{ 90 = 9*10 }}}
(2) {{{ 90 = 90 }}}
OK