Question 132277
Since the problem only talks about 500 buttons and no other number
of buttons, I can call 500 buttons 1 job
(machine A's rate) + (machine B's rate) = (rate running together)
(1 job / x minutes) + (1 job / 2x minutes) = 1 job / 40 minutes)
{{{1/x + 1/(2x) = 1/40}}}
Multiply both sides by {{{2*x*40}}}
{{{80 + 40 = 2x}}}
{{{2x = 120}}}
{{{x = 60}}}
Machine A makes 500 buttons in 60 minutes
Machine B makes 500 buttons in 120 minutes
check:
{{{1/x + 1/(2x) = 1/40}}}
{{{1/60 + 1/120 = 1/40}}}
{{{2/120 + 1/120 = 3/120}}}
{{{1 + 2 = 3}}}
OK