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Circular gears X and Y start rotating at the same time

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fitzpratik
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Circular gears X and Y start rotating at the same time [#permalink] New post   15 Apr 2019, 08:44
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Circular gears X and Y start rotating at the same time at constant speeds. Gear X makes 20 rotations per minute and gear Y makes 60 rotations per minute. How many seconds after the gears start rotating will gear Y have made exactly 120 more rotations than gear X?

A. 3

B. 2

C. 120

D. 180

E. 360

Source: ExpertsGlobal
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Circular gears X and Y start rotating at the same time [#permalink] New post   16 Apr 2019, 12:09
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Work rate of X = 20/60 = 1/3 rotations per second
Work rate of Y = 60/60 = 1 rotation per second

We can think of this problem shrinking-distance problem, where two objects are moving in the same direction and we have to find the time/point where they will meet.

Here Y has to catchup with X, so work rate will be 1-\(\frac{1}{3}\) = \(\frac{2}{3}\) rotations per second

Time taken to do 120 rotations = \(\frac{120}{2}\)* 3 = 180 sec
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Re: Circular gears X and Y start rotating at the same time [#permalink] New post   15 Apr 2019, 09:44
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fitzpratik wrote:
Circular gears X and Y start rotating at the same time at constant speeds. Gear X makes 20 rotations per minute and gear Y makes 60 rotations per minute. How many seconds after the gears start rotating will gear Y have made exactly 120 more rotations than gear X?

A. 3

B. 2

C. 120

D. 180

E. 360

Source: ExpertsGlobal


This question tests your ability to write on your pad and confirm you are answering what the test is asking. The rotations are given in minutes, but it asks how many seconds gear Y will have 120 more rotations. We can write multiples of 60 for y and 20 for x and see that in 3 minutes y will have 180 rotations, and x 60, with a difference of 120 rotations. 3 is not the correct answer however, as there are 180 seconds in 3 minutes. D.
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Re: Circular gears X and Y start rotating at the same time [#permalink] New post   16 Apr 2019, 17:40
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fitzpratik wrote:
Circular gears X and Y start rotating at the same time at constant speeds. Gear X makes 20 rotations per minute and gear Y makes 60 rotations per minute. How many seconds after the gears start rotating will gear Y have made exactly 120 more rotations than gear X?

A. 3

B. 2

C. 120

D. 180

E. 360

Source: ExpertsGlobal


We can use the formula: (difference in work done)/(difference in speeds) = time. So we have:

120/(60 - 20) = 120/40 = 3 minutes

Thus, in seconds, the time is 3 x 60 = 180 seconds.

Alternate Solution:

Notice that it takes gear X 1/20 minutes = 3 seconds to make a complete rotation. Similarly, gear Y makes a complete rotation in 1/60 = 1 second.

Now, let gear Y make 120 more rotations than gear X in t seconds. In t seconds, gear X makes t/3 rotations and gear Y makes t rotations; therefore we must have:

t = t/3 + 120

3t = t + 360

2t = 360

t = 180

Answer: D
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Re: Circular gears X and Y start rotating at the same time [#permalink] New post   09 Jun 2020, 04:28
We know that D=TxS

T for both X and Y is the same and their respective speed is 20rotation per minutes and 60rotation per minutes
The question asks us the time in seconds.
We also know that Dy is equal to D+120 rotation so we can set up the equation

20T=60T - 120

T= 3 minutes which are 180 seconds
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Re: Circular gears X and Y start rotating at the same time [#permalink] New post   03 Jul 2020, 05:12
fitzpratik wrote:
Circular gears X and Y start rotating at the same time at constant speeds. Gear X makes 20 rotations per minute and gear Y makes 60 rotations per minute. How many seconds after the gears start rotating will gear Y have made exactly 120 more rotations than gear X?

A. 3

B. 2

C. 120

D. 180

E. 360

Source: ExpertsGlobal


Gear X = 20 rotations per minute

Gear Y= 60 rotations per minute

difference= 60-20= 40 rotations per minute

40*X=120
X= 3 minutes

3*60= 180 seconds
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Re: Circular gears X and Y start rotating at the same time [#permalink]
03 Jul 2020, 05:12
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