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# Who can solve it?

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Intern
Joined: 15 Aug 2017
Posts: 13

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01 Sep 2017, 11:29
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A certain letter will be sent to potential clients. If 4 computers can make independently 4 letters in 4 minutes, then 100 computers can make 100 letters in exactly how many minutes?
Director
Joined: 21 May 2013
Posts: 613
Re: Who can solve it? [#permalink]

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01 Sep 2017, 11:33
Fran94 wrote:
A certain letter will be sent to potential clients. If 4 computers can make independently 4 letters in 4 minutes, then 100 computers can make 100 letters in exactly how many minutes?

(4 computers* 4 minutes)/4 letters=(100 computers*x minutes)/100 letters

Intern
Joined: 15 Aug 2017
Posts: 13
Re: Who can solve it? [#permalink]

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01 Sep 2017, 12:06
KS15 wrote:
Fran94 wrote:
A certain letter will be sent to potential clients. If 4 computers can make independently 4 letters in 4 minutes, then 100 computers can make 100 letters in exactly how many minutes?

(4 computers* 4 minutes)/4 letters=(100 computers*x minutes)/100 letters

Can you please explain? I thought it was 100
VP
Joined: 22 May 2016
Posts: 1420

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01 Sep 2017, 16:58
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KUDOS
Fran94 wrote:
KS15 wrote:
Fran94 wrote:
A certain letter will be sent to potential clients. If 4 computers can make independently 4 letters in 4 minutes, then 100 computers can make 100 letters in exactly how many minutes?

(4 computers* 4 minutes)/4 letters=(100 computers*x minutes)/100 letters

Can you please explain? I thought it was 100

Fran94 , KS15 set up a proportion, and the answer is correct.

Maybe try it this way: to the standard Rate * Time = Work table, just add one more variable to the left hand side, thus

# of machines M * Rate * Time = Work

Manipulate the equation with four variables (MRT=W) the same way you would with three (RT=W).

Find each machine's individual rate. With the extra variable M, you simply manipulate

M * R * T = W

R = $$\frac{W}{(M * T)}$$

R = $$\frac{4}{(4 * 4)}$$

R = $$\frac{1}{4}$$ = each machine's rate

Now use the rate to find the time for a different number of machines, and a different amount of work.

M * R * T = W

100 * $$\frac{1}{4}$$ * T = 100

T = $$\frac{W}{(M * R)}$$

T = $$\frac{100}{\frac{100}{4}}$$

T = 100 * $$\frac{4}{100}$$

T = 4 minutes

(You could also notice that the LHS is 100/4 = 25, so RHS/LHS = 100/25 = 4 minutes)

Maybe try drawing the table (I do) with the extra variable, and doing the math. The proportional relationship should become clearer.

Does that help?
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Formerly genxer123

Math Expert
Joined: 02 Sep 2009
Posts: 44336
Re: Who can solve it? [#permalink]

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02 Sep 2017, 08:23
Fran94 wrote:
A certain letter will be sent to potential clients. If 4 computers can make independently 4 letters in 4 minutes, then 100 computers can make 100 letters in exactly how many minutes?

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Re: Who can solve it?   [#permalink] 02 Sep 2017, 08:23
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