machine a and machine b process the same work at different rates . machine c processes work as fast as machines a and b combined . machine d processes work 3 times as fast as machine c ; machine d ’ s work rate is also exactly 4 times machine b ’ s rate . assume all 4 machines work at fixed unchanging rates . if machine a works alone on a job , it takes 7 hours . if all 4 machines work together on the same job simultaneously , how many minutes will it take all of them to complete it ?  Choose one:	A) 8	B) 21	C) 24	D) 27	E) 30

Rationale: c = a + b d = 3 c = 3 ( a + b ) = 4 b then b = 3 a and c = 4 a the combined rate of the four machines is a + 3 a + 4 a + 12 a = 20 a machine a can complete the work in 420 minutes , so its rate is 1 / 420 of the work per minute . the combined rate is 20 / 420 = 1 / 21 so the work will be completed in 21 minutes . the answer is b .
Answer: B