Machine A can fill an order of widgets in a hours. Machine B can fill the same in b hours. Machine A & B begin to fill an order of widget at noon, working together at their respective rates. If a & b are even integers, is machine A's rate same as Machine B.
1) Machine A & B finish the order at exactly 4:48pm .
2) (a+b) ^2 = 400
Work/Rate Problem
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- aditiniyer
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We have to see whether a = b given that and b are even integers. We need not find out whether 'a' is greater than 'b' or vice-versa.aditiniyer wrote:Machine A can fill an order of widgets in a hours. Machine B can fill the same in b hours. Machine A & B begin to fill an order of widget at noon, working together at their respective rates. If a & b are even integers, is machine A's rate same as Machine B.
1) Machine A & B finish the order at exactly 4:48pm .
2) (a+b) ^2 = 400
S1: total time, A and B worked = 4.48 pm - 12 pm = 4 hours and 24 minutes = 24/5 hours
Thus, 1/a + 1/b = 5/24
Say, a = b, then 2/a = 5/24
=> a = 48/5 hours, not an even integer. Answer is NO. Sufficient.
S2: (a+b)^2 = 400
=> a+b = 20
If a = b = 10 (both even), the answer is YES.
However, if a = 2 and b = 18 (both even), the answer is NO. No unique answer.
Answer: A
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We are given that machine A can fill an order of widgets in a hours and machine B can fill the same order in b hours. We are also given that a and b are even integers, and we need to determine whether machine A's rate is same as machine B's. Since rate = work/time, the rate of machine A is 1/a and the rate of machine B is 1/b. We need to determine if 1/a = 1/b. However, if 1/a = 1/b, then a = b. So we need to determine if a = b.aditiniyer wrote:Machine A can fill an order of widgets in a hours. Machine B can fill the same in b hours. Machine A & B begin to fill an order of widget at noon, working together at their respective rates. If a & b are even integers, is machine A's rate same as Machine B.
1) Machine A & B finish the order at exactly 4:48pm .
2) (a+b) ^2 = 400
Statement One Alone:
Machines A & B finish the order at exactly 4:48 pm.
Since the machines started working at 12 pm and finished at 4:48, we see that it took the machines 4 hours and 48 minutes to complete the job.
4 hours and 48 minutes = 4 and 48/60 hours = 4 and 4/5 hours = 24/5 hours
Thus, the combined rate is 1/(24/5) = 5/24. Let's now determine whether a = b. Suppose it does and we can make the rates of machines A and B the same; say both rates are 1/a. Thus we have:
1/a + 1/a = 5/24
2/a = 5/24
5a = 48
a = 48/5 = 9.6
However, since we are given that a and b are EVEN INTEGERS, and if both rates were the same, we would NOT PRODUCE an even integer for a or b. Statement one is sufficient for us to say that the rates of machines A and B are NOT equal. We can eliminate answer choices B, C, and E.
Statement Two Alone:
(a+b)^2 = 400
We can take the square root of both sides of the given equation:
a + b = 20
Since a + b = 20, we see that both a and b could be 10, making the rates equal, or a = 8 and b = 12, making the rates NOT EQUAL. Statement two alone is not sufficient to answer the question.
Answer: A
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