(1) Machine A can produce x products in 1hour, machine b can produce x products in 3 hours. If machine A and B work together to produce x products, what is the ratio of the products that the faster machine produces to total products?
A. 1/4
B. 1/2
C. 3/4
D.1
E. 5/4
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jayhawk2001
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Working for 1 hour, we get a total of x + x/3 products when A and B workjc114 wrote:(1) Machine A can produce x products in 1hour, machine b can produce x products in 3 hours. If machine A and B work together to produce x products, what is the ratio of the products that the faster machine produces to total products?
A. 1/4
B. 1/2
C. 3/4
D.1
E. 5/4
together. So, ratio of products from A (the faster one) to the total
products =
x / (x + x/3)
= x / (4x/3)
= 3/4
Is C the answer ?
I guess we can also employ pure POE here. The answer cannot be
greater than 1. So, that leaves out D and E. Also, the ratio cannot be
1/2 (as both machines don't work at same speed). It can't be less than
1/2 as well as we are talking about ratio of faster machine to total.
So, POE would mean C
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Scott@TargetTestPrep
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The rate of machine A is x, and the rate of machine B is x/3. Thus, we see that the faster machine is machine A. If the two machines work together for 1 hour, they will make:jc114 wrote:(1) Machine A can produce x products in 1hour, machine b can produce x products in 3 hours. If machine A and B work together to produce x products, what is the ratio of the products that the faster machine produces to total products?
A. 1/4
B. 1/2
C. 3/4
D.1
E. 5/4
x + x/3 = 4x/3
products. Of those 4x/3 products, machine A will have produced x of them. Thus, the ratio of machine A's product to that of the combined output is:
x/((4x)/3) = 3/4.
Alternate Solution:
Notice that as the two machines operate at constant rates, the ratio of the output of the faster machine (which is machine A) to the total output is the same for any amount time they work together. So, let's calculate the ratio of the products produced by machine A when the two machines together work for 1 hour.
In one hour, machine A will produce 3x products and machine B will produce x products; for a total of 3x + x = 4x products. Of these 4x products, 3x was produced by machine A; therefore the ratio we are looking for is 3x/4x = 3/4.
Answer: C
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