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18 Apr 2025, 20:19
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Made by A in 1 hour: 60
Made by all 3 machines in 1 hour: 228
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
84% (02:48) correct
16%
(02:34)
wrong
based on 483
sessions
History
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Time
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Three machines produce marbles, each at its own constant rate. Machine A can produce in 60 minutes the same number of marbles that machine B produces in 75 minutes. Machine C operates twice as fast as machine A and can complete one full production lot of 90 marbles in 45 minutes.
In the table below, identify the number of marbles produced by Machine A in one hour, and identify the number of marbles produced by all three machines together in one hour. Make only two selections, one in each column.
In the table below, identify the number of marbles produced by Machine A in one hour, and identify the number of marbles produced by all three machines together in one hour. Make only two selections, one in each column.
| Made by A in 1 hour | Made by all 3 machines in 1 hour | |
| 45 | ||
| 48 | ||
| 60 | ||
| 120 | ||
| 171 | ||
| 228 |
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Official Answer
Made by A in 1 hour: 60
Made by all 3 machines in 1 hour: 228
29 Apr 2025, 11:29
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1. The question asks us to calculate the number of marbles machine A / all three machines will make in one hour.
2. First let's find the production rate for all 3 machines. Let machines A, B, and C have rates (number of marbles made per hour) a, b, and c, respectively.
3. Now we can write equations for the information given in the text:
- Machine A can produce in 60 minutes the same number of marbles that machine B produces in 75 minutes. \(a * 1 = b * 1.25\).
- Machine C operates twice as fast as machine A. \(c = 2a\).
- Machine C can complete one full production lot of 90 marbles in 45 minutes. \(c * 0.75 = 90\).
4. \(c * 0.75 = 90 \rightarrow c = 120\), \(c = 2a \rightarrow a = c * \frac{1}{2} = 120 * \frac{1}{2} = 60\), and finally \(a * 1 = b * 1.25 \rightarrow b = a * \frac{1}{1.25} = 60 * \frac{1}{1.25} = 48\).
5. This means that machine A makes a or 60 marbles in an hour and all three machines make a+b+c = 60+48+120 = 228 marbles in an hour.
6. Our answer will be: Made by A in 1 hour - 60 and Made by all 3 machines in 1 hour - 228.
2. First let's find the production rate for all 3 machines. Let machines A, B, and C have rates (number of marbles made per hour) a, b, and c, respectively.
3. Now we can write equations for the information given in the text:
- Machine A can produce in 60 minutes the same number of marbles that machine B produces in 75 minutes. \(a * 1 = b * 1.25\).
- Machine C operates twice as fast as machine A. \(c = 2a\).
- Machine C can complete one full production lot of 90 marbles in 45 minutes. \(c * 0.75 = 90\).
4. \(c * 0.75 = 90 \rightarrow c = 120\), \(c = 2a \rightarrow a = c * \frac{1}{2} = 120 * \frac{1}{2} = 60\), and finally \(a * 1 = b * 1.25 \rightarrow b = a * \frac{1}{1.25} = 60 * \frac{1}{1.25} = 48\).
5. This means that machine A makes a or 60 marbles in an hour and all three machines make a+b+c = 60+48+120 = 228 marbles in an hour.
6. Our answer will be: Made by A in 1 hour - 60 and Made by all 3 machines in 1 hour - 228.
07 Jul 2025, 04:29
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Rate of Machine C = Marbles / Time = 90 marbles / 45 minutes = 2 marbles per minute.
Since Machine C operates twice as fast as Machine A, So, 2 marbles/minute =2×RA
Rate of Machine A (RA ) = 1 marble per minute.
Marbles produced by Machine A in one hour = RA×60 minutes = 1 marble/minute * 60 minutes = 60 marbles.
Machine A produces in 60 minutes the same number of marbles that Machine B produces in 75 minutes
Machine B produces 60 marbles in 75 minutes.
Rate of Machine B (RB) = 60 marbles / 75 minutes.
Simplify the fraction: RB =12/15=4/5 marbles per minute.
RB per hour = 4/5 marbles/minute * 60 minutes/hour = (4 * 60) / 5 = 240 / 5 = 48 marbles/hour.
RCper hour = 2 marbles/minute * 60 minutes/hour = 120 marbles/hour.
Total = 60 + 48 + 120 = 228 marbles.
Number of marbles produced by Machine A in one hour: 60
Number of marbles produced by all three machines together in one hour: 228
Since Machine C operates twice as fast as Machine A, So, 2 marbles/minute =2×RA
Rate of Machine A (RA ) = 1 marble per minute.
Marbles produced by Machine A in one hour = RA×60 minutes = 1 marble/minute * 60 minutes = 60 marbles.
Machine A produces in 60 minutes the same number of marbles that Machine B produces in 75 minutes
Machine B produces 60 marbles in 75 minutes.
Rate of Machine B (RB) = 60 marbles / 75 minutes.
Simplify the fraction: RB =12/15=4/5 marbles per minute.
RB per hour = 4/5 marbles/minute * 60 minutes/hour = (4 * 60) / 5 = 240 / 5 = 48 marbles/hour.
RCper hour = 2 marbles/minute * 60 minutes/hour = 120 marbles/hour.
Total = 60 + 48 + 120 = 228 marbles.
Number of marbles produced by Machine A in one hour: 60
Number of marbles produced by all three machines together in one hour: 228
