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Bunuel , this is a relatively easy question, but one thing that came to my mind:
Usually, we multiply the number of revolutions by 2pie. Why didn't we do it in this problem?

Thank you!
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HWPO
Bunuel , this is a relatively easy question, but one thing that came to my mind:
Usually, we multiply the number of revolutions by 2pie. Why didn't we do it in this problem?

Thank you!

Hi HWPO,

We might use the formula for Circumference (re: C = 2pi(r)) if we were calculating the 'distance traveled' by the rotating gears. Here though, we're not interested in that - we're interested in total revolutions (and since we have the two RATES that the gears are spinning, the actual radii of the gears - and thus, the circumference of the gears - is irrelevant to the calculation).

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EMPOWERgmatRichC
HWPO
Bunuel , this is a relatively easy question, but one thing that came to my mind:
Usually, we multiply the number of revolutions by 2pie. Why didn't we do it in this problem?

Thank you!

Hi HWPO,

We might use the formula for Circumference (re: C = 2pi(r)) if we were calculating the 'distance traveled' by the rotating gears. Here though, we're not interested in that - we're interested in total revolutions (and since we have the two RATES that the gears are spinning, the actual radii of the gears - and thus, the circumference of the gears - is irrelevant to the calculation).

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Rich

Makes perfect sense. Thank you, Rich
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enigma123
Circular gears P & Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15

Aany idea how to solve this?

Note that we are given revolutions per minute and asked about revolutions in seconds. So we should transform per minute to per second.

Gear P makes 10 revolutions per minute --> gear P makes 10/60 revolutions per second;
Gear Q makes 40 revolutions per minute --> gear Q makes 40/60 revolutions per second.

Let \(t\) be the time in seconds needed for Q to make exactly 6 more revolutions than gear P --> \(\frac{10}{60}t+6=\frac{40}{60}t\) --> \(t=12\).

Answer: D.

Hope it's clear.


Hey! I have tried to explain to myself in wording the logic of the function but was never able to really comprehend why the +6 is added to T and not Q in the created function.
I understand that we look for a point in time where t in both gears is equal but revolutions +6 for Q, so why 6 were added to P instead?
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Q rotates 4x as fast as P. Therefore:

Q - - - - - - P
1 rev --> 1/4 rev
4 rev --> 1 rev ==> at this stage Q has 3 more rotations than P. We want 6 more (double the current difference), so;
8 rev --> 2 rev ==> at this stage Q has 6 more rotations than P. So we need to find t for when either Q has completed 8 revolutions or P has completed 2 revolutions

For Q:
40rev --> 1 min
8 rev --> 8/40 = 1/5 min = 12s

(For P: 10 rev --> 1 min, 2 rev --> 2/10 = 1/5 min = 12s)
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P = 10 rev/ min = 10 rev in 60 seconds ( 1 min = 60 sec)

Q = 40 rev/ min = 40 rev in 60 sec ( 1 min = 60 sec)

Difference Q-P = 30 rev ( 40 -10) in 60 sec


Ratio of difference in rev : time 30 rev : 60 sec
1 rev : 2 sec

For differenceof 6 rev 6rev : 12 sec
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enigma123
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15

Hi BrentGMATPrepNow, in conversion of min > second, noticed that some experts here calcuate it as min/60 but some as min * 60 and still arrive at the same answer. Why is that and could you help?

10/60t+6=40/60t --> t=12s.

OR > (40-10) t = 6
t= 1/5 min * 60 > t = 12s
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enigma123
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15

Hi BrentGMATPrepNow, in conversion of min > second, noticed that some experts here calculate it as min/60 but some as min * 60 and still arrive at the same answer. Why is that and could you help?

10/60t+6=40/60t --> t=12s.

OR > (40-10) t = 6
t= 1/5 min * 60 > t = 12s

The formulas seconds = minutes/60 and seconds = minutes * 60 are not both correct.

We can quickly test this by plugging in a certain number of minutes.
For example, let's plug in 2 minutes.
For each "formula," we get:

seconds = minutes/60
seconds = 2/60 = 1/30
So, using this formula, 2 minutes = 1/30 seconds.

seconds = minutes * 60
seconds = 2 * 60 = 120
So, using this formula, 2 minutes = 120 seconds.

As you can see, the first formula does not work
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧

­
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute.

◉ Rate of Gear P = P = 10
◉ Rate of Gear Q = Q = 40

How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

Let time be t mins
=> Revolutions done by Gear P = Rate of P * t = 10 * t = 10t
=> Revolutions done by Gear Q = Rate of Q * t = 40 * t = 40t

Q makes 6 more revolutions than P
=> 40t = 10t + 6
=> 40t - 10t = 6
=> 30t = 6
=> t = \(\frac{6}{30}\) mins = \(\frac{6}{30}\) * 60 sec = 12 seconds

So, Answer will be D
Hope it helps!

Watch following video to MASTER Work Rate Problems

­
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P makes 10rev in 60sec, 1 rev in 6 sec
Q makes 40rev in 60sec, 4 rev in 6 sec
So at 6 sec, the difference in rev is 3 , and will keep growing by a multiple of 3 in 6 sec increments
At 12 sec, it will be 6
enigma123
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15
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Hi!
We can think on a very simple approach of relative speed.
Every 60 seconds, Gear Q gains 30 revolutions(40-10) and hence in other words this
extra 30 revolutions is completed in 60 seconds
extra 1 revolutions by Q is completed in 60/30 or 2 seconds
extra 6 revolutions by Q is completed in 6x2 = 12 seconds.

Hope this helps.
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