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Seb’s watch gains 5 seconds in every 3 hours, whereas Lewis’ watch

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Seb’s watch gains 5 seconds in every 3 hours, whereas Lewis’ watch  [#permalink]

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New post Updated on: 11 Aug 2018, 12:39
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Question Stats:

56% (02:28) correct 44% (02:36) wrong based on 73 sessions

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Seb’s watch gains 5 seconds in every 3 hours, whereas Lewis’ watch loses 10 seconds in every 2 hours. If both watches are set to the correct time at 1 a.m. Sunday, then at what earliest time they will have a difference of 9 minutes among them?

    A. 7 a.m. Wednesday
    B. 10 a.m. Wednesday
    C. 7 p.m. Wednesday
    D. 10 p.m. Wednesday
    E. 7 a.m. Thursday


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Originally posted by EgmatQuantExpert on 30 Jul 2018, 21:54.
Last edited by EgmatQuantExpert on 11 Aug 2018, 12:39, edited 1 time in total.
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Re: Seb’s watch gains 5 seconds in every 3 hours, whereas Lewis’ watch  [#permalink]

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New post 30 Jul 2018, 22:11
1
2
B

9 minutes = 540 seconds
In every 6 hours, difference increases by 40 seconds.
In 78 hours, by 520 seconds

Only 20 more seconds required.

In next 3 hours, Seb's watch would gain 5 seconds and Lewis's watch would lose 15 seconds (10 seconds in 2 hours is same as 5 seconds in 1 hour)
Difference = 5 + 15 = 20 seconds

Total hours passed = 78+3 = 81
81 hours from 1am Sunday is 10am Wednesday.

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Re: Seb’s watch gains 5 seconds in every 3 hours, whereas Lewis’ watch  [#permalink]

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New post 30 Jul 2018, 22:57
9 minutes = 9*60 = 540 seconds.

Seb’s watch gains 5 seconds in every 3 hours
Every hour Seb's match gain 5/3 seconds

Lewis’ watch loses 10 seconds in every 2 hours
Every hour Lewis’ watch loses 10/2 = 5 seconds

Relative difference per hour = 5 + 5/3 = 20/3 Seconds

Time taken to gain 540 seconds = 540/(20/3) = 540*3/20 = 81 hours

81 Hours = 72 Hours (3 24 Hour day) + 9 Hours =>

1 AM + 9 Hours = 10 AM, which is 3 days later i.e. Wednesday.

Option B
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Seb’s watch gains 5 seconds in every 3 hours, whereas Lewis’ watch  [#permalink]

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New post 10 Aug 2018, 05:58

Solution



Given:
    • Seb’s watch gains 5 seconds in every 3 hours
    • Lewis’ watch loses 10 seconds in every 2 hours
    • Both watches are set to the correct time at 1 a.m. Sunday

To find:
    • At what earliest time the watches will have a difference of 9 minutes among them

Approach and Working:
    • A difference of 9 minutes is equivalent to 60 x 9 = 540 seconds.

Now, Seb’s watch gains 5 seconds in every 3 hours.
    • Hence, in 1 hour, it will gain \(\frac{5}{3}\) seconds.

Similarly, Lewis’ watch loses 10 seconds in every 2 hours.
    • Hence, in 1 hour, it will be losing 5 seconds.

    • Therefore, in 1-hour time, the difference created between the watches = \(\frac{5}{3}\) – (-5) = \(\frac{20}{3}\) seconds

Now, we can say, to create a difference of \(\frac{20}{3}\) seconds, we need 1 hour.
    • So, to create a difference of 540 seconds, we need 540/(\(\frac{20}{3}\)) = 81 hours.

From 1 a.m. Sunday, 81 hours forward will be 10 a.m. Wednesday.

Hence, the correct answer is option B.

Answer: B


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Seb’s watch gains 5 seconds in every 3 hours, whereas Lewis’ watch &nbs [#permalink] 10 Aug 2018, 05:58
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