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Working alone at its constant rate, machine A produces k car

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Working alone at its constant rate, machine A produces k car [#permalink]  12 Sep 2017, 13:30
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Question Stats:

85% (01:03) correct 14% (01:10) wrong based on 96 sessions
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?

[Reveal] Spoiler: OA
6 minutes

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Founder
Joined: 18 Apr 2015
Posts: 13918
GRE 1: Q160 V160
Followers: 315

Kudos [?]: 3684 [0], given: 12942

Re: Working alone at its constant rate, machine A produces k car [#permalink]  12 Sep 2017, 13:46
Expert's post
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
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Re: Working alone at its constant rate, machine A produces k car [#permalink]  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?

[Reveal] Spoiler: 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

[Reveal] Spoiler:
6

Cheers,
Brent
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Re: Working alone at its constant rate, machine A produces k car   [#permalink] 13 Sep 2017, 12:50
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