Question 468959
Let d=distance, r=speed, t =time
d = r*t
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Trip 1:
t represents time to travel lake at 12 mph
{{{d = 18(t-(1/4))}}}
Goal is to solve for d, so get t in terms of d
{{{d/18 = t - (1/4)}}}
{{{(d/18)+(1/4) = t}}}
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Trip 2:
{{{d = 12t}}}
{{{d/12 = t}}}
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Set equations equal to each other, since both are equal to t
{{{d/12 = (d/18)+(1/4)}}}
Eliminate fractions by multiplying equation by 36
LCM of 4,12,18 is 36 --> 4*9=36, 12*3 = 36, 18*2 =36
{{{3d = 2d + 9}}}
Subtract 2d on both sides
{{{d = 9}}}
Length of lake is 9 mi.