Question 409525
Let {{{w}}} = windspeed
Against wind: {{{220 - w}}} mi/hr
With wind: {{{220 + w}}} mi/hr
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Against wind:
(1) {{{330 = (220 - w)*t}}}
with wind:
(2) {{{550 = (2230 + w)*t}}}
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Solve both equations for {{{t}}}
(1) {{{t = 330/(220 - w)}}}
(2) {{{t = 550/(220 + w)}}}
Therefore:
{{{330/(220 - w) = 550/(220 + w)}}}
{{{330*(220 + w) = 550*(220 - w)}}}
divide both sides by {{{10}}}
{{{33*(220 + w) = 55*(220 - w)}}}
{{{7260 + 33w = 12100 - 55w}}}
{{{88w = 12100 - 7260}}}
{{{88w = 4840}}}
{{{w = 55}}}
The wind speed is 55 mi/hr
check answer:
(1) {{{t = 330/(220 - 55)}}}
{{{t = 330/165}}}
{{{t = 2}}} hrs
and
(2) {{{t = 550/(220 + 55)}}}
{{{t = 550/275}}}
{{{t = 2}}} hrs
OK