Problem Solving

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

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

Using Catch Formula:

Time to Catch = GAP/Diff of speed

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

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.

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.

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

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