Question 110491
N = nancy's time working alone
T = Terry's time working alone
{{{(1/N) + (1/T) = 1/7}}}
{{{N = 2T}}}
{{{(1/(2T)) + (1/T) = 1/7}}}
multiply both sides by {{{(2T)(T)*7}}}
{{{7T + 14T = 2T^2}}}
{{{2T^2 - 21T = 0}}}
{{{T(2T - 21) = 0}}}
T = 0 is a solution, but disregard it
{{{2T = 21}}}
{{{T = 10.5}}}days Terry's time working alone
{{{N = 2T}}}
{{{N = 21}}}days Nancy's time working alone
check
{{{(1/N) + (1/T) = 1/7}}}
{{{(1/21) + (1/10.5) = 1/7}}}
{{{(1/21) + (2/21) = 3/21}}}
OK