Circular gears

Ashetty wrote:Circular gears P and Q rotating at same time at constant speeds, Gear P makes 10 revolution per minute & gear Q makes 40 revolutions per minute. How many seconds after 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
ANS: D.12

First rewrite speeds as revolutions per second (since the question uses these units)

Gear P makes 10 revolution per minute, in other words 10 revolutions per 60 seconds.
To determine the number of revolutions per 1 second, divide 10 by 60, to get 10/60 revolutions per second (a.k.a. 1/6 revolutions per second)

Gear Q makes 40 revolution per minute (or 40 revolutions per 60 seconds).
To determine the number of revolutions per 1 second, divide 40 by 60, to get 40/60 revolutions per second (a.k.a. 2/3 revolutions per second)

Now let t = the time in seconds

The number of revolutions gear P makes in t seconds = (1/6)t
The number of revolutions gear Q makes in t seconds = (2/3)t

We need to determine the number of seconds it takes such that gear Q makes exactly 6 more revolutions than gear P.

So, we want to know the value of t such that:
(Q's revolutions) - (P's revolutions) = 6
Or . . . (2/3)t - (1/6)t = 6
To solve, first multiply both sides by 6 to get: 4t - t = 36
3t = 36
t = 12

It will take 12 seconds, so the answer is D

Cheers,
Brent

Ashetty wrote:Circular gears P and Q rotating at same time at constant speeds, Gear P makes 10 revolution per minute & gear Q makes 40 revolutions per minute. How many seconds after 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
ANS: D.12

P takes 1/6 revolutions per second.
Q takes 2/3 revolutions per second.
Let after T seconds the gears start rotating will gear Q have made exactly 6 more revolutions than gear P.
Then after x seconds, 2T/3 - T/6 = 6
3T/6 = 6
T = 12

The correct answer is D.