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Circular gears P and Q start rotating at the same time at constant spe
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23 Jul 2022, 08:22
23 Jul 2022, 08:22
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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
A. 6
B. 8
C. 10
D. 12
E. 15
Re: Circular gears P and Q start rotating at the same time at constant spe
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24 Jul 2022, 16:33
24 Jul 2022, 16:33
Expert Reply
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.
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.
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Re: Circular gears P and Q start rotating at the same time at constant spe
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07 Sep 2024, 04:13
07 Sep 2024, 04:13
1
↧↧↧ 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
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
