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by bacali » Mon Dec 01, 2008 3:29 pm
Machine A, operating alone at its constant rate, produces 500 feet of a particular fiber in 2 hours. Machine B, operating alone at its constant rate ,produces 500 feet of the same fiber in 3 hours. Machine C, operating alone at its constant rate. Produces 500 feet of the same fiber in 5 hours. How many hours will it take machines A. B, and C, operating together at their respective constant rates, to produce 1000 feet of the fiber?



A. 60/31 B. 15/7 C. 25/11 D. 10/2 E. 20/3



OA: A
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by dmateer25 » Mon Dec 01, 2008 3:52 pm
Take the inverse of each of these rates and set them equal to (1/t) to find the time it takes working together.

For 500 feet:

1/2 + 1/3 + 1/5 = (1/t)

15/30 + 10/30 + 6/30 = 1/t

31/30 = 1/t
30/31=t

so for 500 ft it takes 30/31. For 1000 ft it would be (30/31)*2=60/31
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by cramya » Mon Dec 01, 2008 8:06 pm
Another way

Rate A = 500/2= 250 (FOR 1 HOUR)
Rate B = 500/3 (FOR 1 HOUR)
Rate C = 500/5 = 100

Add the rates when they work together

rate*time = work
(250+500/3+100)*time = work
(250+500/3+100)*time = 1000

time = 3000/1550 = 60/31

A)
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