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 rates, to produce 1,000 feet of the fiber?
I solved it as below, however the official explanation was quite different than my calculations. Can you make a few suggestions, how you would solve it, pls? Thanks!
rates:
1/2 -> machine A
1/3 -> machine B
1/5 -> machine C
1/2 + 1/3 + 1/5 = 5/6 + 1/5 = 25/30 + 6/30 = 31/30
30/31*2 = 60/31
I solved it as below, however the official explanation was quite different than my calculations. Can you make a few suggestions, how you would solve it, pls? Thanks!
rates:
1/2 -> machine A
1/3 -> machine B
1/5 -> machine C
1/2 + 1/3 + 1/5 = 5/6 + 1/5 = 25/30 + 6/30 = 31/30
30/31*2 = 60/31
