Question 1168449

The local post office has three machines for sorting the mail. If each works alone, machine A can accomplish the job in 2 hours, machine B in 3hours and machine C in 1 1/2 hours. Machine C begins the job and works for half an hour when it suddenly breaks down. Machine A and B are then activated and work together to complete the sorting process. How long does it take for machines A and B to finish.
<pre>Machine A does job in 2 hours, or {{{1/2}}} of job in 1 hour
Machine B does job in 3 hours, or {{{1/3}}} of job in 1 hour
Machine C does job in {{{1&1/2}}} hours, or {{{matrix(1,5, 1/(1&1/2), or, 1/(3/2), or, 2/3)}}} of job in 1 hour
With machine C working for {{{1/2}}} hour, and with T being the time machines A & B take to finish the job, we get: {{{matrix(2,3, (1/2)(2/3) + T(1/2 + 1/3), "=", 1, 1/3 + T/2 + T/3, "=", 1)}}}
2 + 3T + 2T = 6 ------- Multiplying by LCD, 6
3T + 2T = 6 - 2
5T = 4
Time machines A and B took to complete job, or {{{highlight_green(matrix(1,7, T, "=", 4/5, hour, or, 48, minutes))}}}</pre>