Circular gears P and Q start rotating at the same time at co

[imane81]

thank you for your help on this one...

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 geat P ?
A. 6
B. 8
C. 10
D.12
E.15

[komal]

thank you for your help on this one...

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 geat P ?
A. 6
B. 8
C. 10
D.12
E.15

Every minute, gear Q makes 30 more revolutions than P (40-10=30). Since the rates are constant, Q would make 6 more revolutions in 1/5 min (30/6=5). 1/5 min is 12 sec (60/5=12).

12 sec.

[ajith]

thank you for your help on this one...

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 geat P ?
A. 6
B. 8
C. 10
D.12
E.15

P does 1/6 revolutions a second
Q does 2/3 revolutions a second

after x seconds 2x/3-x/6 = 6
3x/6 =6
x = 12

[harsh.champ]

thank you for your help on this one...

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 geat P ?
A. 6
B. 8
C. 10
D.12
E.15

Another approach that I can suggest is that of relative speed.
The relative speed of Q with respect to P is 30 revolutions/minute..[S=30]
For making 6 relative revolutions[D = 6],Time = Relative Distance/Relative Time = 6/30 = 1/5 minute = 1/5 x 60 = 12 seconds.Hence,D.

[thephoenix]

revolution by P in 1 swc=1/6
and by Q is 2/3

say after x sec the lead of Q IS 6

IN X SEC p REVOLVES X/6
AND Q REVOLVES 2X/3

AS THE DIFF SHUD BE 6----------> 2X/3 - X/6=6--------->X=12