revolutions per minute

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josh80: Senior | Next Rank: 100 Posts; Posts: 72; Joined: Sun Nov 03, 2013 9:29 am; Thanked: 1 times

by josh80 » Wed Dec 11, 2013 5:26 pm

Circular gears P & Q start rotating at the same time at constant speeds. Gear P makes 10 revs/minute and gear Q makes 40 revs/minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revs than gear P?

6
8
10
12
15

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Wed Dec 11, 2013 10:38 pm

This can be solved in about 30 seconds:

Because the speeds are constant, the difference between the revolutions of the wheels increases at a constant rate.

In one minute, gear Q (40/minute) will have revolved 30 more times than gear P (10/minute).
Because 6 is exactly one-fifth of 30, it will take exactly one-fifth as much time to create a difference of six revolutions.

so the answer is one-fifth of a minute, or 12 seconds.

Check:
their speeds in seconds are 10/60 = 1/6 revolution per second for P, and 40/60 = 4/6 revolution per second for Q.

In 12 seconds, P will have revolved 1/6 * 12 or 2 times, while Q will have revolved 4/6 * 12 = 8 times. Thus in 12 seconds Q will have made exactly 6 more revolutions than P.

Answer: 6

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Wed Dec 11, 2013 11:58 pm

Using Catch Formula:

Time to Catch = GAP/Diff of speed

=> 6/30 = 1/5 minutes ==> 12 seconds

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abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 amFollowed by: 11 members; Location: NY; Thanked: 28 times

by abhasjha » Thu Dec 12, 2013 12:44 am

40- 10 = 30 revolutions more in 60 seconds

so 1 revolution more in 60/30 = 2 seconds
so 6 revolutions more in 2x 6 = 12 seconds

answer D.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Dec 12, 2013 4:09 am

josh80 wrote:Circular gears P & Q start rotating at the same time at constant speeds. Gear P makes 10 revs/minute and gear Q makes 40 revs/minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revs than gear P?

6
8
10
12
15

When elements compete, SUBTRACT THEIR RATES.

Every minute Q makes 40 revolutions and P makes 10 revolutions.
The difference between their rates is 40-10 = 30.
Thus, every minute Q makes 30 more revolutions than P.

To determine how many seconds it will take Q to make 6 more revolutions than P, set up a proportion:
30 revolutions/60 seconds = 6 revolutions/x seconds
30x = 360
x = 12.

The correct answer is D.

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Sun Dec 15, 2013 10:42 pm

I have a qustion here,
time of q for one revs = 40/60 = 2/3
in 12 seconds q made 2/3*12= 8 revs
in 12 sesonds p made mearly 1.25 revs , so differance comes out to be more then 6

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Dec 15, 2013 11:43 pm

vipulgoyal wrote:I have a qustion here,
time of q for one revs = 40/60 = 2/3
in 12 seconds q made 2/3*12= 8 revs
in 12 sesonds p made mearly 1.25 revs , so differance comes out to be more then 6

the part in Red is incorrect; refer the part green below
P, 10Rev/min ==> 1 sec = 10/60
Q, 40rec/min ==> 1 sec = 40/60
In 12 seconds
P = 10/60 * 12 = 2
Q = 40/60 * 12 = 8
Difference = 6

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