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It takes Sarah 12 minutes to do one oil change, and it takes Alice 10

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It takes Sarah 12 minutes to do one oil change, and it takes Alice 10  [#permalink]

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New post 07 Jan 2015, 07:42
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Tough and Tricky questions: Word Problems.



It takes Sarah 12 minutes to do one oil change, and it takes Alice 10 minutes. If Sarah and Alice both begin doing oil changes at exactly 9:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?

A. 10:00 a.m.
B. 10:42 a.m.
C. 12:00 a.m.
D. 1:00 p.m.
E. 2:00 p.m.

Kudos for a correct solution.

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Re: It takes Sarah 12 minutes to do one oil change, and it takes Alice 10  [#permalink]

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New post 07 Jan 2015, 08:39
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Sarah = 12 minutes
Alice = 10 minutes

12*10 = 60 minutes, they will meet at 60 minutes (Sarah completed 5, Alice completed 6)

9:00am + 60 minutes = 10am - A


Bunuel wrote:

Tough and Tricky questions: Word Problems.



It takes Sarah 12 minutes to do one oil change, and it takes Alice 10 minutes. If Sarah and Alice both begin doing oil changes at exactly 9:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?

A. 10:00 a.m.
B. 10:42 a.m.
C. 12:00 a.m.
D. 1:00 p.m.
E. 2:00 p.m.

Kudos for a correct solution.
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Re: It takes Sarah 12 minutes to do one oil change, and it takes Alice 10  [#permalink]

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New post 07 Jan 2015, 09:36
Option A is right.

Key here is to find out the Least common multiplier of 12 and 10 -> 60
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Re: It takes Sarah 12 minutes to do one oil change, and it takes Alice 10  [#permalink]

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New post 07 Jan 2015, 20:51
1
Answer = A. 10:00 a.m.

LCM of 10 & 12

10 = 2 * 5

12 = 2 * 2 * 3

LCM = 2 * 2 * 3 * 5 = 60 = 1 hour

0900 + 0100 = 1000AM

Another method

Write the table of 10 & 12; catch up the first common multiple

10 ...................... 12
20 ...................... 24
30 ...................... 36
40 ...................... 48
50 ........................ 60
60
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Re: It takes Sarah 12 minutes to do one oil change, and it takes Alice 10  [#permalink]

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New post 09 Jan 2015, 07:01
Bunuel wrote:

Tough and Tricky questions: Word Problems.



It takes Sarah 12 minutes to do one oil change, and it takes Alice 10 minutes. If Sarah and Alice both begin doing oil changes at exactly 9:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?

A. 10:00 a.m.
B. 10:42 a.m.
C. 12:00 a.m.
D. 1:00 p.m.
E. 2:00 p.m.

Kudos for a correct solution.


OFFICIAL SOLUTION:

(A) Since Sarah will finish s oil changes after s × 12 minutes and Alice will finish c oil changes after c × 10 minutes, they both will finish doing an oil change at the same time when s × 12 = c × 10. Since s and c must be integers (they represent the number of oil changes finished) this question is asking you to find a common multiple of 12 and 10. The question asks for the first time they will finish a car simultaneously, so you must find the least common multiple. The least common multiple of 12 and 10 is 60, so in the context of the question, this would be 60 minutes, or one hour. Therefore, the first time they will finish changing the oil of a car at the same time is 9:00 + 1 hour, or 10:00 a.m. The answer is (A).
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Re: It takes Sarah 12 minutes to do one oil change, and it takes Alice 10  [#permalink]

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New post 16 Dec 2018, 21:30
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Re: It takes Sarah 12 minutes to do one oil change, and it takes Alice 10   [#permalink] 16 Dec 2018, 21:30
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