Question 17553
Distance=600miles,Speed=x mph
Time taken=(600/x)hours
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Second case:
Distance=600miles,Speed=(x+20)mph
Time=(600/x+20)hours which we know is 1 hour less than the first case
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So we get,
{{{ (600/x) - (600/(x+20)) = 1 }}}
<font color=blue><b>[This is your required equation]</b></font>
{{{ (600(x+20)-600x)/(x(x+20)) = 1 }}}

{{{ (600x+12000-600x)/(x^2+20x) = 1 }}}

{{{ 12000 = x^2+20x }}}

{{{ x^2+20x-12000 = 0 }}}

This is a quadratic in x and can thus be solved as:

{{{ x^2+20x-12000 = 0 }}}

{{{ (x-100)(x+120) = 0 }}}

So we get x=100 or -120 mph

This speed cannot be negative, thus <font color=blue><b> x=100</b></font>
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Hope this helps,
prabhat