Question 175969
Call the smallest integer {{{n}}}
The next larger will be {{{n + 2}}}
The next larger will be {{{n + 4}}}
Given:
{{{n + n + 2 + n + 4 = 27}}}
{{{3n + 6 = 27}}}
{{{3n = 21}}}
{{{n = 7}}}
The integers are 7, 9, and 11
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{{{d = r*t}}}
Given:
{{{t[1] = 3/4}}}hr
{{{t[2] = 9/60}}}hr
In the 1st case,
{{{d = r*(3/4)}}}
In the 2nd case,
{{{d = (r + 12)*(3/4 - 9/60)}}}
{{{d = (r + 12)*(15/20 - 3/20)}}}
{{{d = (r + 12)*(3/5)}}}
The distances are the same in each case, so
{{{r*(3/4) = (r + 12)*(3/5)}}}
Multiply each sides by {{{20}}}
{{{15r = 12*(r + 12)}}}
{{{15r = 12r + 144}}}
{{{3r = 144}}}
{{{r = 48}}} mi/hr
And, since
{{{d = r*(3/4)}}}
{{{d = 48*(3/4)}}}
{{{d = 36}}} mi answer
check answer:
{{{d = (r + 12)*(3/5)}}}
{{{d = (48 + 12)*(3/5)}}}
{{{d = 60*(3/5)}}}
{{{d = 36}}}mi
OK