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Working alone at its constant rate, machine A produces k car
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12 Sep 2017, 13:30
12 Sep 2017, 13:30
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Question Stats:
88% (01:02) correct
11% (01:28) wrong based on 168 sessions
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Working alone at its constant rate, machine A produces k car parts in 10 minutes. Working alone at its constant rate, machine B produces k car parts in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce k car parts?
enter your value as minutes
enter your value as minutes
Show: :: OA
6 minutes
Practice Questions
Question: 5
Page: 126
Difficulty: medium
Question: 5
Page: 126
Difficulty: medium
Re: Working alone at its constant rate, machine A produces k car
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12 Sep 2017, 13:46
12 Sep 2017, 13:46
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Explanation
When the machines work simultaneously, the rate at which the parts are produced is the sum of these two rates, which is \(\frac{k}{10}\) + \(\frac{k}{15}\) = \(k *\) (\(\frac{1}{10}\) + \(\frac{1}{15}\)) = \(k *\) (\(\frac{25}{150}\)) = \(\frac{k}{6}\) parts.
\(T = \frac{W}{R}\) = K/K/6 = 6
When the machines work simultaneously, the rate at which the parts are produced is the sum of these two rates, which is \(\frac{k}{10}\) + \(\frac{k}{15}\) = \(k *\) (\(\frac{1}{10}\) + \(\frac{1}{15}\)) = \(k *\) (\(\frac{25}{150}\)) = \(\frac{k}{6}\) parts.
\(T = \frac{W}{R}\) = K/K/6 = 6
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Re: Working alone at its constant rate, machine A produces k car
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13 Sep 2017, 12:50
13 Sep 2017, 12:50
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Carcass wrote:
Working alone at its constant rate, machine A produces k car parts in 10 minutes. Working alone at its constant rate, machine B produces k car parts in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce k car parts?
enter your value as minutes
enter your value as minutes
Show: :: OA
6 minutes
Another approach is to assign a "nice" value to the entire job. That is, a nice value that works well with the two given times (10 minutes and 15 minutes)
Let's say k = 30
So, machine A produces 30 car parts in 10 minutes
So, machine A's RATE = 3 parts per minute
And machine B produces 30 car parts in 15 minutes
So, machine B's RATE = 2 parts per minute
So, the COMBINED rate of both machines = 3 + 2 = 5 parts per minute
How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce k (30) car parts?
Time = output/rate
= 30/5
6 minutes
Answer:
Show: ::
6
Cheers,
Brent
