Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?
+357 One man can finish in X days.
2 machines finish in 13 days, so 1 machine finishes in 26
3 men and 8 machines finish in 1/2 the time it takes 3 machines and 8 men.
Because of that 3/M + 8/26 = 2(8/M + 3/26)
3/M + 4/13 = 16/M + 3/26
16/M – 3/M = 4/13 – 3/13
13/M = 1/13
M = 169
Number of men to finish the job is: 13 days = 169/13 = 13
Yay!
