Question 170727
well we know that distance equals rate times time. d=rt
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In our case distance is the same under both scenarios 600 miles.
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what is different is the speeds and thus the times as speed and time are inversely related.
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so in the first trip lets call the rate r and the time t.
in the second scenario the rate would be r+20 and the time is t-1.
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600=rt....................eq 1
600=(r+20)(t-1)...........eq 2
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lets rewrite eq 1 as t=600/r and place that value into eq 2
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{{{600=(r+20)((600/r)-1)}}}
{{{600=(r+20)((600-r)/r)}}} multiply by r
{{{600r=(r+20)(600-r)}}} multiply factors on right side of eq
{{{600r=600r-r^2+12000-20r}}} combine like terms on one side of equation
{{{r^2+20r-12000=0}}}
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throw out the negative speed{{{system(r=100mph,r=-120mph)}}}
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so speed on first trip is {{{100}}}mph and on second trip is {{{100+20=120}}}mph
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*[invoke quadratic "r", 1, 20, -12000]