Question 1132269

It takes Phoebe and Karen 2 hours and 40 minutes in making a long gown.working alone Karen would need 4 hours longer than Phoebe to finish the job.How long will each of them to do the job alone?
<pre>Let time Karen takes be H
Then time Phoebe takes = H  -  4
And, Karen and Phoebe can do {{{matrix(1,3, 1/H, and, 1/(H  -  4))}}} of job in 1 hour, respectively
We then get: {{{matrix(1,3, 2&2/3 * (1/H) + 2&2/3 * (1/(H - 4)), "=", 1)}}} ======> {{{matrix(1,3, (8/3) * (1/H) + (8/3) * (1/(H - 4)), "=", 1)}}} ======> {{{matrix(1,3, 8/(3H) + 8/3(H - 4), "=", 1)}}}
8(H  -  4) + 8H = 3H(H  -  4) -------- Multiplying by LCD, 3H(H  -  4)
{{{matrix(1,3, 8H - 32 + 8H, "=", 3H^2 - 12H)}}}
{{{matrix(1,3, 3H^2 - 12H - 16H + 32, "=", 0)}}}
{{{matrix(1,3, 3H^2 - 28H + 32, "=", 0)}}}
{{{matrix(1,3, 3H^2 - 24H - 4H + 32, "=", 0)}}}
3H(H  -  8) - 4(H  -  8) = 0
(H  -  8)(3H - 4) = 0_____H - 8 = 0         OR         {{{matrix(1,4, H, "=", 4/3, "(IGNORE)")}}} 
H, or time Karen takes: {{{highlight_green(matrix(1,2, 8, hours))}}}
Time Phoebe takes: {{{highlight_green(matrix(1,4, 8 - 4, "=", 4, hours))}}}