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Working alone at a constant rate, Machine A can produce 15 widgets in

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Math Expert
Joined: 02 Sep 2009
Posts: 58381
Working alone at a constant rate, Machine A can produce 15 widgets in  [#permalink]

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18 Jan 2019, 01:10
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Difficulty:

35% (medium)

Question Stats:

69% (02:11) correct 31% (02:21) wrong based on 62 sessions

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Working alone at a constant rate, Machine A can produce 15 widgets in 2 minutes. Working alone at a constant rate, Machine B can produce 20 widgets in 3 minutes. If the two machines start working at the same time, after how many minutes will Machine A have produced 40 more widgets than Machine B?

A 12
B 24
C 36
D 48
E 60

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Re: Working alone at a constant rate, Machine A can produce 15 widgets in  [#permalink]

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18 Jan 2019, 08:09
Bunuel wrote:
Working alone at a constant rate, Machine A can produce 15 widgets in 2 minutes. Working alone at a constant rate, Machine B can produce 20 widgets in 3 minutes. If the two machines start working at the same time, after how many minutes will Machine A have produced 40 more widgets than Machine B?

A 12
B 24
C 36
D 48
E 60

rate for A = 15/2
rate for B = 20/3

solve using answer options we see
that at 48 mins ; A would have made 40 more widgets than B
15*48/2 = 360
20*48/3 = 320

IMO D
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Joined: 15 Feb 2018
Posts: 365
Re: Working alone at a constant rate, Machine A can produce 15 widgets in  [#permalink]

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18 Jan 2019, 20:26
Working alone at a constant rate, Machine A can produce 15 widgets in 2 minutes.
Machine A rate: $$\frac{15 (widgets)}{2 (minutes)}$$

Working alone at a constant rate, Machine B can produce 20 widgets in 3 minutes.
Machine B rate:$$\frac{20 (widgets)}{3 (minutes)}$$

If the two machines start working at the same time, after how many minutes will Machine A have produced 40 more widgets than Machine B?
rate·time=work completed
We have the respective rates from above.
Machine A and B both work for the same time (we'll denote this time with x).
We know the work completed is a difference of 40

Machine A Rate·x - Machine B Rate·x=40 widgets
$$\frac{15 (widgets)}{2 (minutes)}·x - \frac{20 (widgets)}{3 (minutes)}·x=40 (widgets)$$
eliminate units for simplicity. Just remember x will be units of time
$$\frac{15x}{2}-\frac{20x}{3}=40$$
$$\frac{45x}{6}-\frac{40}{6}=40$$
$$\frac{5x}{6}=40$$
5x=240
x=48 minutes

D
Re: Working alone at a constant rate, Machine A can produce 15 widgets in   [#permalink] 18 Jan 2019, 20:26
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