Working simultaneously at their respective constant rates, machine A and B produces 20 widgets in c hours. Working alone at its constant rate, Machine A produces 20 widgets in 'a' hours.In terms of a and c, how many hours does it take Machine B, working alone at its constant rate, to produce 10 widgets  Options:
A) ac/a+c
B) 2ac/a+c
C) ac/2a+2c
D) ac/2a-2c
E) ac/2c-2a
Let the individual rates be R(a) and R(b) for machines a and b respectively. Given than combined rate is 20 widgets in c hours =&gt; 20/c   R(a) + R(b) = 20/c   Also given is the individual rate for machine a = R(a) = 20/a   Therefore, R(a) + R(b) = 20/c =&gt; 20/a + R(b) = 20/c =&gt; R(b) = 20/c - 20/a = 20(a-c)/ac = 20/(ac/(a-c)), which basically means that b produces 20 widgets in ac/a-c Hrs. We have to calculate how much does it take to produce 10 widgets. So divide the rate by 2 which gives us ac/2(a-c).   Hence the answer is ac/2a-2c
<result>D</result>
Working simultaneously at their respective constant rates, machine A and B produces 20 widgets in c hours. Working alone at its constant rate, Machine A produces 20 widgets in 'a' hours.In terms of a and c, how many hours does it take Machine B, working alone at its constant rate, to produce 10 widgets