Question 1170604

It takes Robert 9 hours longer to construct a fence than it takes Eldin. If they work together, they can construct the fence in 20 hours. How long would it take each, working alone, to construct the fence?
<pre>Let time it takes Robert to do the job, be R
Then time it takes Eldin is: R - 9
Therefore, Robert can do {{{1/R}}} of job in 1 hour, while Eldin can do {{{1/(R - 9)}}} of job in 1 hour
We then get the following equation: {{{matrix(1,3, 1/R + 1/(R - 9), "=", 1/20)}}}
20(R - 9) + 20R = R(R - 9) ------- Multiplying by LCD, 20R(R - 9)
{{{matrix(4,3, 20R - 180 + 20R, "=", R^2 - 9R,
40R - 180, "=", R^2 - 9R,
0, "=", R^2 - 9R - 40R + 180,
0, "=", R^2 - 49R + 180)}}}
(R - 45)(R - 4) = 0
Robert's time to complete job, alone: {{{highlight_green(matrix(1,2, 45, hours))}}}                OR                 R = 4 (ignore)
Eldin's time to complete job, alone: {{{highlight_green(matrix(1,4, 45 - 9, "=", 36, hours))}}}